Suppose that f(x) = 5x² + 2x. Use the limit definition of the derivative to answer the following: (A) Find the slope of the line tangent to f(x) at x = –3. (B) Find the instantaneous rate of change of f(x) at x = –3. (C) Find the equation of the line tangent to f(x) at x = –3. y =

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: Find the derivative of function defined as follows.

A: we have to find the derivative of the given function . y=2x7-8x

Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

A:

Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

A:

Q: Find the derivative of function defined as follows.

A:

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: Find f(x) if f(0) = 0 and the tangent line at (x, ƒ (x)) has the slope x(x² + 2}°.

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 7x +3x…

A:

Q: Q2. Find the slope of the tangent line to the function f(x)= at x 4 by using the 2Vx definition of…

A: Given that,

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

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 6x +…

A: Formula use Instataneous rate of change og f w.r.t x at a i f'(a) = lim f(a+n)-f(a) / n…

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

A:

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: Find f'(10) directly from the definition of the derivative given f(x) = vx – 1.

A: Given, f(x) =x-1  We have to find f'(10)

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Find the derivative of the following function using the limiting process. f(x) = 1/x2

A:

Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

A:

Q: Find the derivative of function defined as follows.

A: Derivative of the function can be found with the help of differentiation of the function.…

Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: As per instructions we solve it by limit definitely of derivative .

Q: Find the equation of the line tangent to the graph of f(x)=(lnx)^2 at x=3.

A:

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

A:

Q: Compute for the derivative of the function below for x = 1. f(x) = 2xe

A: Solution: dydxx=1=2xex

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

A:

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 11.

A: Here we have to use limit definition to find derivative

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: find the derivative using the definition ƒ(t) = 1/2t + 1

A: Given:ft=12t+1Derivative definition:f'x=limh→0fx+h-fxh

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: For the function given by g (x) = x2 + 2x +1, use the limit definition of the derivative to compute…

A: Please refer the attached image for complete solution.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(r) =…

A: The limit definition of the derivative is

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

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: 2x f{X) = 1+ X

A: Given: f(x)=2x1+x

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = V7x +3…

A:

Q: Find f(x) if f(1) 7 1 and the tangent line at (x, f(x)) has slope f(x) =

A: We know that the slope of tangent at any point to the curve of a function is given by the derivative…

Q: Suppose f(x)= √1 − 3x a. Use the definition of derivative to find the slope of the tangent line to…

A: Given: f(x)= √1 − 3x To find: a. Use the definition of derivative to find the slope of the tangent…

Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

A:

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

A:

Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: Find the equation of the tangent line to the graph of the function f(x)=x+1x−6 at the point (0,−16).

A: Equation of tangent is y-y1=m(x-x1) where m is the slope.

Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

A:

Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does…

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change c f(x) = 4x + 7x…

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x