Express the function y= 6(x- 2) as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(z). f(u) = help (formulas) g(z) = help (formulas)

Q: Using the limit definition find the derivative of the function f(x)=3x+2.

A:

Q: x³+3x f(x) = 2-4x+3

A: Given that fx=x3+3xx2-4x+3   Quotient rule for differentiation. ddxuv=v·ddxu-uddxvv2 Here,  u=x3+3x,…

Q: Perform a first derivative test on the function f(x) = x/64 - x ;[-8,8]. a. Locate the critical…

A:

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A:

Q: [CLO-2] Find the derivative of f (x) = x −x5 e 2x + 3 1-5x4 x-x5 x-5x5 2/x −x5 1-5x4 Vx-x5 −5x4…

A:

Q: Exercise III: Implicit differentiation Assume that a factory can produce a quantity 2x3 + x?y + y°…

A: Given The equation is 2x3+x2y+y3=c Where  x  is the number of skilled workers  and   y is the number…

Q: Plot the function f(x) x-2x2-10sin2x- e0.9x and its derivative for -2sx54 in one figure. Plot the…

A: Given,fx=x3-2x2-10sin2x-e0.9xf'x=3x2-4x-20sinxcosx-e0.9x· 0.9

Q: Finding the derivative of f(x) = 2x2+3x+2, using definition of derivative

A:

Q: Function f(x) = 2x^3 - 36x^2 + 210x - 7 has two critical numbers. Smaller number= Larger number=

A:

Q: Find the derivative of the function. y =    8x2 − 5 2 − x   3    y' =

A:

Q: f(x) = 2+6x -x'use the limit definition of derivative t

A:

Q: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

A: The given function is fx=ax+1,    x<-1x2-3,     x>-1 To find: Value of parameter a

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: QI Find f'(2) for (x³ – x)(x² + 2)(x² +x – 1) f(x) = %3D x + 2

A: Here I am attaching image so that you understand each and every step.

Q: Using the criterion of the first and second derivatives, find the graph of the function b) F(x) =…

A:

Q: x2-4 %3D b) By use derivative sketch the function f(x) 2x

A:

Q: Use the second derivative to discuss concavity. The second derivative is y’’ ={2x(x2+3)}/ (x2-1)3

A: given,  y''=2xx2+3x2-13 we have to discuss the concavity using second derivative.

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A: Solution is here

Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x > 0 is the output…

A: We will use the basic knowledge of functions and derivatives of functions to answer this question.…

Q: (3-x, xs1 Consider the function given by f (x) = Is the function continuous, %3D x -x+1, x>1…

A:

Q: Perform a first derivative test on the function f(x) = x/25 - x;(-5,5]. a. Locate the critical…

A:

Q: (b) f(x) = (3x – 2a²)³

A:

Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x 2 0 is the output…

A:

Q: 4. Find the derivative. x? + 6x – 5 (a) 5х -1 (b) ƒ(x) = (3xr² – 5x - 7)' Us e chain rule (c) y =(x-…

A: Topic:- derivatives

Q: 2x+1 Use Derivative Rules to find the derivative of g(x) x2-1

A:

Q: . Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.)…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: Perform a first derivative test on the function f(x) = x/100 - x² ;[- 10,10]. a. Locate the critical…

A:

Q: Using the 2nd Derivative Test, find all relative extrema of f (x) = 2x - 3x-4. Justify your answers.

A:

Q: Find derivative by Quotient Rule and by simplifying first.

A:

Q: x² + 3 Find the derivative of the functionf (x) = V2x +5 3x2+10x – 13 A. f'(x) = f"(x). %3D…

A:

Q: erify the IVT for the specified function f, the interval (a,b), and the indicated value w. 1. f(x)=…

A: The IVT(Intermediate Value Theorem) says if f(x) is continuous on the interval [a,b] and…

Q: Find the first and second derivatives of the function. f(x) = x5 − x4 + 7x3 − 8x2 + 4x − 15 f '(x)…

A:

Q: x2 -4 b) By use derivative sketch the function f(x) %3D 2x

A:

Q: F(x)=8x-2; X=2, x=3 How do I find the average rate of change and net rate

A: Given that F(x)=8x-2; X=2, x=3  To find the average rate of change and net rate

Q: Use the First Derivative Test to find the local maximum and minimum values of the function. (Enter…

A:

Q: Use the Chain Rule to find the derivative of the function. y = (4x2 − 5)3 y' =

A: Solved below

Q: h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in…

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: V. HIGHER DERIVATIVES AND CHAIN RULE 2. y = x²(x – 1)³(2x – 5)² 3. f (x) = V1 + V1-x

A:

Q: ind an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Given

Q: Find the equation of the tangent line to the graph of the function f(x)=(x^2+9)(x-3) at the point…

A: Given : f(x) =(x2+9) (x-3)

Q: Suppose f(x) = 2ax3 + b3x − 4c where a, b and c are real constants. Suppose that f has a horizontal…

A: f(x) = 2ax3 + b3x - 4c    Differentiating wrt x,    f'(x)  =  6ax2 + b3

Q: Find an equation of the line tangent to the graph of f(x) = 5 – 5x at (3, – 40). The equation of the…

A:

Q: 2z - 8z Use the chain rule to find the derivative of f(x) = 3e f'(x) =

A:

Q: x2-3 b) By use derivative sketch the function f(x) x-2

A:

Q: The derivative of the function f(x) = -5x? – 16x + 22 by definition of derivatives f(x + h) – f(x) |…

A:

Q: Find an equation of the line tangent to the graph of f(x) = 3– 7x at (-4,- 109). The equation of the…

A:

Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A: Solution is given below...

Q: Find the derivative of the function using the definition of a derivative. State the domain of the…

A: Plug f(x) and f(x+h) in the definition of derivative.Express them as difference of cubesApply…