Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = √(4 - x2) on the interval [ - 2, 2]. Explain how this can happen.

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find the average rate of change for function over the given interval.

A: Given  y=3x-2.

Q: Find the derivative of the function f(x) = V (x² – 3)° at x = 5 at x = – 2. f'( – 2) = Preview

A: Given :    f(x) = x2-356    , x = -2

Q: What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]

A:

Q: What is the average rate of change of the function f(t) = -3t between t--4 and f--3?

A: what is average rate of change of the function f(t)=t2 -3t between t=-4 and t=-3   answer  put t=-4…

Q: Find all points on the interval (1, 3) at which the slope of the tangent line equals the average…

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Q: Find the average rate of change of f(x) with respect to x on the interval. f(x)= x^2 -5x+1; [-3,0]

A: f(x)=x2-5x+1;-3,0 We need to find the average rate change of f(x)

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 7x +3x…

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 6x +…

A: Formula use Instataneous rate of change og f w.r.t x at a i f'(a) = lim f(a+n)-f(a) / n…

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 7x² +…

A:

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

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Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

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Q: Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the…

A: To find- derivative of the given function using definition  of limit.

Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

A:

Q: Find the derivative of the function.

A: Given: y=ln(x4)(1,0)

Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

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Q: Find the average rate of change of f(x) = 8x2 - x:(a) From 1 to 2       (b) From 0 to 1     (c) From…

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Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

A:

Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

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Q: Find the derivative of the function. y = In(Icsc(7x)|) y'(x) =

A:

Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

A:

Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: Calculate the derivative of the function below using the quotient rule. 28 y = Vx + 8x7 f(æ) = %3D…

A:

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = V7x +3…

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Find the derivative of the function.

A:

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: Find the derivative of f(x) = ln v4 – x2 %3D

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

A:

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

Q: What is an average rate of change of function f(x) over the interval [1, 6]?

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A:

Exponential Growth Model

The relation that represents an exponential function is: