Find the average rate of change of f(x)=5x^2-3 on the interval [2,t]. Answer with an expression involving t

Q: Find the average rate of change of f(x) = x² - x + 1 from x, = 1 to x, = 3. %3!

A: We have to find the average rate of change of function fx=x2-x+1 from x1=1 to x2=3. We know average…

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

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

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Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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

A: The given function y and the values of x between which the average rate of change of y is to be…

Q: Use differentials to estimate the value. estimate =  exact value =

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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: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Find the average rate of change of the function over the interval [-2, 1] f(x) = 2.x³ – 5.x +3

A: To determine the average rate of change of the below function over the interval [-2,1]. fx=2x3−5x+3

Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

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

A: We are given the function f(x)=5x5+3x3+2x+1 and the step size as h=0.5. As we are given no…

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: What formula will describe the average rate of change of f(x) = 3* over the interval [0, 3]? Don't…

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Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos…

A: Given, g(t)=2+cost, -π,π The average rate of change of function f(x) over an interval [a,b] is,…

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: Find the derivative of f(x)=ex/(sqrt x) at x=1. Round your answer to 4 decimal places.

A: Find the derivative of f(x) = ex/(sqrtx) at x=1 round your answer to 4 decimal places. We know that…

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at 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: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

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 average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

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

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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: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Compute the average rate of change of f(x) = x2-1/x on the interval of [2,4]. Please show me each…

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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]?

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Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

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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 average rate of change of the function on the interval specified Y=1/x on [1,3]

A: We know that ,The average rate of change of function over an interval a,bis given by f(b)-f(a)b-a

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

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: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Let f(x)= 2x^3+3x^2-12x on [1,3] What is the average rate of change in f on [1,3]?

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

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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