Find the average rate of change of the function f(x) = x2-40x+28 over the interval [10, 50].

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

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 ) = 3 x over the interval [ 2 , 5 ]

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Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: Find the derivative of the function f(x) = e(z²-3z).

A: The given exponential function has one independent variable which is x.

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 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: Find the derivative of the function. x² F(x) e dt %3D F'(x) =

A: The fundamental theorem of Calculus says: If F(x)=∫h(x)g(x)f(t)dt⇒F'(x)=f(g)g'-f(h)h' Here,…

Q: Find the derivative of the function. Q(x) = V ex + x Q'(x) = %3D

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Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

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Q: Consider the function f (x) = x2. Calculate the rate of change of f (x) at x = 1, and compare your…

A: Consider the function f (x) = x2  To Calculate the rate of change of f (x) at x = 1.

Q: What is the derivative of y = V(x? V(a2 – 1) (x + 1) ? -

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Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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Q: Use the second derivative test to find the local extrema for the function f(x,y) = x² +y³ + 2xy – 3x…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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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: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Find the total a.f(x, y) = ex² + y² 2 derivative of t

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Q: Find the nth-order derivative of the function y=(3x2−2x)lnx, x>0.

A: Use the product rule

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: Find the derivative of the function: f(x)= e^x÷x^2

A: Given,

Q: What is the instantaneous rate of change of f(x) = V +2-3 at %3D x = -2?

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Q: Determine the 3rd derivative of the function y=x3/x+2 at x=−1.

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Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

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Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

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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: Find the derivative of the function. f(x) = ex2 + 2 %3D f'(x)

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Q: Find the derivative of the function. y = 7х + V 7x + V7x

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Q: Find the first derivative of the function * 4 f (x) = Væ + 4

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Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

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Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

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Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

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 first derivative. (a) y=x* (b) y =xnx 2.

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Q: Find the derivative of the function. f(z) = V9 + VI+ VE f (x) =

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Q: Find the derivative of the function.

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

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 of the function. F(x) etd dt F'(x) =

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Q: Find the derivative of the function. f(x) = /7+ V5+ VI f '(x) = %3D

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Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: Find the derivative of the function f(x) = 9r( – 5x + 6z). %3D f'(x) =

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Q: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

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Q: Find the derivative of the function. f(x) = /2 + V1+ Va f (x) = ||

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)