Consider the graph of f' (x). At what value (or values) of x do f (x) have a local maximum?

Q: Find the absolute maximum value of the function y=xV3x-x² on the interval [0, 3].

A:

Q: For the function, f(x) = 9x² – x³ - a. Use the derivative to find all critical points b. Classify…

A:

Q: Sketch the graph of a function ƒ that has a local maximum valueat a point c where ƒ'(c) = 0.

A: If at x=c , there is a local maximum value, then x=c is a critical point. That means f'(c)=0 will be…

Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: Determine whether the following statement is true or false, and explain why. The absolute maximum of…

A:

Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

A:

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: 1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) =…

A:

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: Find the absulote maximum of x40-x20 on the interval [0,1],also find its absolute maximum value

A:

Q: Sketch the graph of f(x) = sin¬'(x² + y²) by analyzing its level curves.

A:

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: 2. Let f(x) = Determine the exact location of any turning points. Use the second derivative to…

A: We can solve this as follows:

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Sketch the graph of a function on [-1, 2] that has anabsolute maximum but no absolute minimum.

A: According to the given information, it is required to sketch the graph of the function on [-1,2]…

Q: Find the x-coordinates of the absolute extrema of f(x) = -x² + 7x on the interval [1, 7]. Absolute…

A: f(x)=-x2+7x differentiating both side f'(x)=-2x+7 now f'(x)=0 -2x+7=0 x=3.5 So x=1, 3.5, 7

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: At what value of x is f minimum?

A: To find: The value of x for which f is minimum. Calculation: It is observed from the graph that the…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: Locate the critical points of the function f(x) = x + 2x + 6x - 4 and use the second derivative test…

A: We solve the equation f'(x)=0 to find the critical points of the function. If a is a critical point,…

Q: Find the absolute minimum and absolute maximum values of f on the given interval. fx) =Dx -In(7x),…

A:

Q: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

A:

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

A:

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find the absolute maximum of x40-x20 on the interval [0,1].Find also its absulute maximum value

A:

Q: Find a function y whose graph passes through the point (1, =) and satisfies x2y' = y.

A: NOTE: Refresh your page if you can't see any equations. .

Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local…

A: Find first derivative.

Q: Find the derivative of the function by the limit process. PX) = x - 9x + 1

A:

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

A:

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: Find the x value where the function g(x) = xe-lx attains a local maximum. Enter the exact answer. If…

A: Differentiate y and by solving y'=0 obtain critical points. Check sign of y'' on critical points -…

Q: Use the second derivative test to locate all local extrema for the function f(x)=x3−32x2−18x. At…

A:

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the solution to the equation 2x² - 4x + 1 = 0 using simpsons rule with an lower a and upper…

A: Given , f(x)=2x3-4x+1 we have to use Simpsons rule to find solution with lower limit is 1 and upper…

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum…

A: Given: fx=x3+ax2+bx To find a, b such that function has local maxima at x = -1 and local minima x =…

Q: The function h(x) = x³ + 28x4 – 1311x³ has a critical point at x = 19. Use the second derivative…

A:

Q: What conditions must be met to ensure that a function has anabsolute maximum value and an absolute…

A: Given, To write conditions that must be met to ensure that a function has anabsolute maximum value…