Use the definition of the derivative to compute the derivative of the function f(x)at an arbitrary point x. Evaluate the limit byхusing algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).f(x + h) – f(x)f' (x) = limlimPart 3: The tangent lineNow let's calculate the tangent line to the function f(x)at x = 6.хa. By using f' (x) from part 2, the slope of the tangent line to f at x = 6 is f' (6) =b. The tangent line to f at x = 6 passes through the point (6, f(6)) =on the graph of f. (Enter a point in theform (2, 3) including the parentheses.)c. An equation for the tangent line to f at x = 6 is y =

Answered: Image /qna-images/answer/ad1f4a2d-6ec1-4fbc-8adf-c5b255603545.jpg

Answered: Use the definition of the derivative to…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

See similar textbooks

Similar questions

What is the purpose of the Intermediate Value Theorem?
use the definition of the derivative to compute the derivative of the function f(x)=1−2x2 at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). f′(x)=limh→0(f(x+h)−f(x)h)=limh→0( )= .
Let f(x)=4x 2+12x−2Using the definition of derivative, f'(x)=limh→0 f(x+h)−f(x) /h,enter the expression needed to find the derivative at x=3.f'(x)=limh→0 After evaluating this limit, we see that f'(x)= Finally, the equation of the tangent line to f(x), in point-slope form, where x=3 is ------
Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the specific point x=2x=2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find an equation of the tangent line to the graph of y=3-x/2x+3 at (-1,4) using f'(a)= lim as h->0 f(a+h)-f(a)/h
Find the derivative of f(x) = 1/√(x + 1) at x = 0 using the definition of the derivative as a limit. Be sure to justify your computations. Specifically, if at any point you evaluate a limit by inserting a value, explain WHY it is possible to do that.
Let f(x)=1/x Using the definition of derivative at point f’(a)=lim f(x)-f(a)/x-a f’(3)=lim x->3___ After evaluating the limit we see that f’(3)=____ Finally the equation of the tangent line to f(x) where x=3 is ___
Use the limit definition to compute the derivatives at the given value of a: 1) f(x)= sqrt(3x-4) for a = 2 2) f(x) = 3x-5/x-2 for a = 1 Use the limit definition to find the slope of the tangent line at a, then find the equation of the tangent line to f at x = a: 1) -3/x-1 at a=4
(a)Find the equation of the tangent line to the curve f(x)=6x^2-5x+3 at the point where x=2. (Use the Basic Differentation Rules to find f'(x). That is, do not use the limit definition (b)Find the equation of the tangent line to thefunction: f(x) = 2x-1/x+2 when x=3
Please provide on how you did it step by step. Use one of the two limit definitions of the derivative to find the derivative of f(x)=7/x at x=3
find the derivative of the function f(x)=x^2 -2x using the definition of the derivative (a process that requires a limit)
for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find an equation of the tangent line to the graph of y=3-x/2x+3 at (-1,4)

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS