F(x) = 2ax^3 + b^3x – 4c where a, b and c are real constants. Suppose that f has a horizontal tangent line at x = 2, and that the tangent line to f at x = 0 is given by y = 8x + 4. Use the given information to find all possible values for a, b, and c. Explain your reasoning and show your work.

Q: Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Given f(x)=(1+2x2)(x-x2) By Product rule,…

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Q4. Find by implicit differentiation of 2x - 3y = 4

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Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: 5. Find the derivative by using the quotient rule. 3x - 2 (a) 2x +3 V+2 (c)- 3+2x (b) x +1 x+2 (d):

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Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

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Q: Use the chain rule to find the derivative of 13 f(x) = 3(6x* – 5a³)* You do not need to expand out…

A: Given that:f(x)=36x4-5x313To find f'(x)

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Q: 9. Use the 2nd derivative to find the inflection point for f(x) = x³ – 6x2 – 4x +3 %3D

A: We will find the point of inflection as following.

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 2. Y = (7x³ + 3)6 ; y"

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Q: Find equation of tangent y=x³-4x+1 at point (2,1)

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

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Q: Find the derivative of f(x) = (2x+1)³(3x - 1)³. Show all your work and factor the result completely

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Q: ction defined by f(x) = x2 – 3x + 4 at (-1, 2). Write

A: we have to find the slope of the line tangent to the graph of the function defined by  f(x) = x2 –…

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Q: Find the derivative by using the quotient rule. 3x-2 (a) 2x +3 Jx +2 (c) x2 3+2x (b) x² +1 (d) *+2

A: Given: a)  3x−22x+3b)  3+2xx2+1c)  x+2x2d)  x+2x

Q: Find the derivative of the function. Provide the solution in factored form. f(x) = 2x(x³ – 2)6 %3D

A:

Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

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A: In this question the given function is y=(x2-5)3x2+3 we have to find y' In positive exponents only

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: Find the second derivative of the function. f(x) = 5(2 − 7x)4   Show your work

A: y''=?

Q: Use the product rule to find the derivative. y= (4x +5)(5x-2) y'= %3D

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Q: Find the derivative of by using the product rule. * (1+ væ³) (x-3 – 2a) y =

A: Consider the provided equation, y=1+x3x-3-2x3 Find the derivative of using the product rule. The…

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A: The objective is to find the equation of tangent line.

Q: find the critical points and apply the Second Derivative Test (or state that it fails).…

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Q: find tangent line to the curve y=3x/7-x at a point of (-3,2/7)

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Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

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Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the derivative of y = (x2 + 4)(x³ + 3) in two ways. (a) by using the Product Rule y' = (b) by…

A: Given function is  Differentiating with respect to x by using product rule of differentiation, we…

Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

A:

Q: Find f' (8) from f(x) = V7x – 2 using the definition of a derivative. (Do not include "f'(8) =" in…

A: This question is related to deivative.

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

A:

Q: Find the derivative of the function xA F(x): - 4x³ + Vx x2 in two ways. Show that your answers are…

A: Given function is : Fx=x4-4x3+xx2 Differentiating the Fx using quotient rule ,…

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A: Given, f(x)=2xln2x To find the derivative of f(x).

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

Q: B. Use the product and quotient rule to get the derivative of the followin 1.Differentiate ( 3x+1) (…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: What rule should be used in getting the derivative of a.)y = x^8 + 2x^6 - x^3 - 4x  b.)…

A: a) y=x8+2x6-x3-4xb) y=2x5+x-3x3c) f(x)=1-2x2

Q: find the critical points and apply the Second Derivative Test (or state that it fails). y = 6x^3/2 −…

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