If f and g are two functions defined by f(x) = 3x +5 and g(x) = r+ 1, then g(f(x)) is %3D o 9,2 + 30x + 26 o 9, + 26 O+3x + 6 O 3x + 8 * Previous

Q: a. f,(Xx)=x f2(x)=x² fa(x)=1-2x² b. f,(x)= e3x f2(x)=e5x fg(x)= e=* C. f,(x) = x-1 f2(x) = x'/2…

A: We have to choose the function that is linearly dependent on the given interval

Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

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Q: f(x) = 3x + 7     g(x) = 4x + 5   and   h(x) = 3x – 5                                           3…

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Q: f(x) = 3x + 5 g(x) = 4x² – 2 %3D h(x) = x² – 3x + 1 Find f(x) - g(x) – h(x). O - 5x + 6x + 6 O -5x +…

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Q: Compute f'(x) a.) f(x) = (x2+1)e-x^2 b.) f(x) = (4e-x-

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Q: (r-1) (x-1) If f(x) = (2x+5) and g(x) = then the function (2) (x) is (2x-5) (2x+5) a) (E) (x) =…

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Q: f(x) = 1 – 2x g(x) = -x2 + 3x h(x) = %3D Зх— 2 4. (f • g)(x) 5. (gof)(x) 6. (ho h)(x) 1. (f +g)(-2)…

A: We have to find (f+g)(-2) , fg3 and g.h12   According to Bartleby guidelines , We can solve only 3…

Q: If f(x) = and g(x) = 5x I +1 , then (f o g)(x) is I+3 4x + 2 16х + 2 4x +1 16х + 1 4x +4 16х + 1 4x…

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Q: f(x)=4x+2 g(x)=-x^2+9x-2g(x)=−x2+9x−2 \text{Find: } f(x) \cdot g(x)Find: f(x)⋅g(x)

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Q: Solve the equation below giving an explanation. Thanks.

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Q: If f(x)= x - 4 and g(x)= Vx-2; which of the following is equal to х — 2 Option 1 – 4(SF 2) X - х — 2…

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Q: The function f(x)=2x^3−24x^2+72x−2 has two critical numbers. The smaller one equals=     and The…

A: We have to find critical numbers  First we have to differentiate of f(x) with respect to x  After…

Q: if f(x)+g(x)= 3x +2 and g(x) = x - 1 then f(x)= %3D а. 2х+3 O b. 3x+2 О с. 3х-2 O d. x+4

A: Given,f(x)+g(x)=3x+2g(x)=x-1f(x)=?

Q: If f (x) = x²cos-(x² – 4), what is f'(x)? 2x3 o f'(x) = 2xcos-'(x² – 4) – V 1-(x²-4)² 2x3 o f'(x) =…

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Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

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Q: f(x)=−4x+4​,g(x)=−5x2+5x−4​,andh(x)=−3x2+8​, find h(−1​).

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Q: Find the critical numbers of the function. (E F(x) = x4/5(x – 5)² %3D

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Q: 2. If f(x) = x-1 and g(x) = - x2+ 2 a) Find (fog)(x)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 19. f(x) = x - 4, g(x) = Vx + 5, x 2 -5 %3D

A: Consider the functions f(x) = x – 4, g(x) = √(x + 5), x ≥ –5

Q: 3h(2)+4g(1) h(x) = {-3x forx= 2} g(x) = {x2+2  forx=3}

A: Given,          hx=-3xfor x<24x+1for x≥2          gx=x2+2for x<3x3for x≥3

Q: If (x) = 2x-6 and g(x) = 3x+ 9, find (f- g)(x). %3D | O A. (f- g)(x) = x+ 15 O B. (f- g)(x) = 5x + 3…

A: Given: fx=2x-6 and gx=3x+9

Q: If f(x)=2x−2f(x)=2x-2 and g(x)=x+1g(x)=x+1, then f(x)=g(x)f(x)=g(x) when x = − 2x = − 1x = 3x = 4.

A: it seems like to find the value of x for which both functions are equal.      given'…

Q: If f(x) = 3x-1 +4 and g(x) = 4x-7, what is (f- g)(x)? %3D O A. (f-g)(x) = 3x-1 - 4x- 3 %D B.…

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Q: If f(x) = -1) (2x+5) and g(x) = (Zx+5) then the function (fg)(x) is (Zx-5) %3D %3D

A: Given,          fx=x-12x+5 and gx=2x+52x-5

Q: If f(x) = x²-x+3, then f(-2x) equals A. 4x² - 2x + 3 B. -4x² + 2x + 3 C. 4x² + 2x + 3 D. 2x² + 2x +…

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Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

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Q: (3x3 + 6x2 + 9x + 2) (22 – 1)3 1. Let f(x) = 3x +2 with f'(x) = 3x2 + 4x +3 and f"(x) = 2- %3D -1…

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Q: Determine

A: We will find the critical points by equating the derivative to zero.

Q: Find the critical points of the functionf (x) = 4x³ – 48x+2. O a. 2,3 O b. -2,-1 O C. -3,3 O d. -2,2

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Q: 0, x4. then P(2<X <4) is equal to

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the critical numbers of the functions. a) f(x) = 3x + 4x b) f(x) = x3 – 3x² – 5x c) f(x) = 3x3…

A: We have to find

Q: If f(x) = 2x+11 then we can write %3D (x-1)(x²+x+1) Select one: O f(x) = 4 + x+1 x+x+1 O f(x) = +…

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Q: Iff(x) = 1 %3D Зх-1 and g(x) = f-' (x), find g' (x). 1 o g'(x) = -, 3x2 o g(x) %3D뉴 1 2r2 1 o g'(x)…

A: Given f(x)=y=13x-1f-1(x):Replace x with y and solve for yx=13y-13y-1=1x3y=1x+1y=x+13x

Q: Find Critical numbers of the given function: x² +5 f(x) = %3D x - 2

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Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

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Q: What are the critical points for the function f(x) = x³ + 9x² + 15x – 8 %3D None x = -1 and x = -5 x…

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Q: The function f(x) = 2x³ – 27x² + 48x 1 has two critical numbers. - The smaller one is x = and the…

A: We have to find the critical points for the function f(x)=2x3-27x2+48x-1.

Q: 1. Which pair of functions is equivalent? a. fx) = - 8x - 5x – 3 g(x) = 8x + 5x + 3 c. Ax) = (-6x +…

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Q: If f(x) = 3x – 2 and g(x) = x + 1, then (f(g))-'() equals O 1– x O x +1 O x – 1 1 O (3x – 1) 3

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Q: Vx+5-5 1. f(x): at (-5,-1) х-20 V16-x2 2. f(x) = at (-3,-1) х+1 V16-x3 3. f(x) = at (-3,-1) х+1 х-16…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The function f(x) = 2x³ – 27x2 + 48x – 3 has two critical numbers. - The smaller one is x = and the…

A: We have to find critical numbers for the function: fx=2x3-27x2+48x-3 We know that critical points of…

Q: 3) If h(x) = 3x –4 f (x ) = 4 x + 6 g (x) = - 2 x- 4 Composition of functions а. h(5) b. g (h ( 5))…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: |x + 2, x> 0 讨论函数f(x) = 在x=0的连续性. х — 2, х <0 -

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Q: Example 3 Minimise F= -Xi-3x +2xa Subject to: 2xi +x: S15 X - 3x2 -X S 6 -x1 +x +2x52 X XX 20…

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Q: 4. Use a calculator. f(x)= 2x-x g(x) =-x -1 %3D

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Q: If f(x) = 4x – 1 and g(x) = Va2 +1, then f(g(x)) is - Oy = (4x – 1) Vx² +1 Oy = 4Vx2 +1–1 4x-1 Oy=…

A: Given fx=4x-1, gx=x2+1To find f(g(x))

Q: Find (f o g)(x). f(x) = 5x - 2, g(x) = – x² + 4x - 1 O -5x? +20x -7 %3D %3D |3| O -25x2 + 40x - 13 O…

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Q: The antiderivative of the function f(x) = -.9 + 10x³ 9. is -6 2.5x4 + c -6 + 2.5x4 + c -10 + 1.5x* +…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.