The function f(x) = 5x + 2 is one-to-one. a. Find an equation for f', the inverse function. b. Verify that your equation is correct by showing that f (f¯"(x)) =x and f'(f(x)) = x. - 1 1 a. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression.) O A. f(x) = , for x# B. f'(x) = for x2 OC. f'(x)= for xs x-2 D. f'(x) = for all x b. Verify that the equation is correct. = f'(O = f and Substitute. Simplify. The equation is II II

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A: We find the limit of the ratio of the two functions

Q: he derivative of f(t) is given by the following function: (9-9x^2)/(e^x+1) when will the number be…

A: The derivative of the function is given as, f'(x)=9-9x2ex+1 For extrema, we need to solve f'(x) = 0…

Q: х7 + 5x6 — х3 f(x) = x?

A:

Q: Find the second derivative of the function. 20 (2-0) 20 dr 2 O A. do 2 1 B. do? O OC. do 1 OD. do?

A: Given:  A function is given by,r=1+2θ2θ2-θ To Find: The second derivative of the given function…

Q: 2. Find the derivative of f (t) = (1²-3)° and simplify your answer as much as possible.

A: We have, f(t)=t2+3(t2-3)2   If we f(x)g(x) form, then the derivative of the function will be,…

Q: Consider the following function. g(x) = -x2 + 9x + 6 Find the first and second derivatives of the…

A: The function is given by gx =-x2+9x+6 To evaluate : The interval where the function is concave…

Q: Given the function​ f, find the slope of the line tangent to the graph of f^-1 at a specified point…

A: Given,f(x) = (x + 1)^2 for x >= -1; (1, 0)First find the inverse of the function.Let y=f(x)then

Q: For the function f(X) = ax3 +ba2 +cx, find the second derivative, f"(X). Here a,b and c are…

A: Given Function,F(x) = ax3 + ba2 + cx

Q: Given the function y=x5+2x3+3x. Find the derivative of the inverse function at x=1.

A: Here, f(x) = y=x5+2x3+3x and a = f(x)|x = 1 = 1 + 2 + 3 = 6

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: x+D メD

A: To Determine: we have a function then find the derivative Given: we have a function Z(x)=Hxx-D2+x2…

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A: fx=x2  &  gx=2x Concept used: Let fx & gx be positive for x sufficiently large. fx grows…

Q: Find a formula for the nth derivative y^n of the function y=(x+5)^1/2

A:

Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: Find the derivative of f(x)=x^2 e^2.5x

A: Given problem:- Find the derivative of f(x)=x2 e2.5x

Q: Find the requested value of the second derivative of the function. 3 f(x) = x* + 4x° - 4x + 4; Find…

A:

Q: For what values is the function f(x)= ln(x+1)/x^2+1 continous? Can you please explain how to…

A: If , g(x) is continuous and h(x) is continuous. Then g(x) / h(x) is continuous.where h(x) not equal…

Q: Find the derivative of the algebraic function.

A: Given: f(x)=4-3x-x2x2-1

Q: 1. Find the derivative of the function f (x) = e2x + 5* + x3

A:

Q: 3e* Find the first derivative: f(x) = x (x+1)

A:

Q: Find the second derivative of the function. f(x) = (3 + 2x)e−3x

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: Consider the following functions (on the given interval, if specified). Find the derivative of the…

A: Given information: f1x=x+2

Q: Find the SECOND derivative of the given function. (b) g(x) = x+2

A:

Q: Find the first derivative of the following functions and simplify your answer. y=* 5x-2 y=(2x2 –…

A: Solution: The objective is to find the derivatives of the given functions

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

A:

Q: Find the anti-derivative of the function and evaluate. g(x)=2x g(0)=7

A:

Q: How to solve the derivative of this

A:

Q: Find the derivative of the function g(x) = 300(4 – e-0.1x)

A: The solution is given as follows

Q: Consider the following functions (on the given interval, if specified). Find the derivative of the…

A: The given function is fx=3x-4. Its corresponding inverse function is f-1x=4+x3.

Q: For what values of x is the derivative of the function 2x - 3x equal to 14?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the derivative of the function. g(x) = 500(5 – e-0.1x)

A: Given,           g(x)=5005-e-0.1x

Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 .  Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: f(x) = e*

A:

Q: 8. y (1 + x³)(3 – 2x) 10. y = (x2 + 3)(x² – x + 1

A:

Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

A:

Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

A:

Q: Find the third derivative of the given function. 8 f(x)

A: This question can be solved using the concept of third order derivatives.

Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

A:

Q: 1 Find the derivative of the function : ƒ(x ) = V |2x + 3

A: The given function is: f(x)=12x+3 Let, u=2x+3. So, f(u)=1u=u-12 and u=2x+3

Q: y = (1+x)² 2 x² 2

A:

Q: Given the function y=x2−x. Find the derivative of the inverse function at x=1.

A:

Q: 4. Calculate the derivative of the following functions, and find a formula for their inverse: (a)…

A:

Q: Find the first and second derivatives of the function. 14. f(x)= x to the 7/2+x to the 5/3-x to the…

A:

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A:

Q: 3 If f( – 6) = 3, and f'( – 6) = %3D Let f'(x) be the inverse function of f(x). (f¯')'(3) = Write…

A:

Q: Find the derivative of the function. f(x) = e-4x

A: The given function is:fx=e-4x