Learning Target D1: I can find the derivative of a function, both at a point and as a function, using the definition of the derivative. Consider the function f(x) 5x²+2x+5. 1. Set up, but do not evaluate, the limit that would compute f'(2) (the derivative of f at x = = 2) = 2. Set up, but do not evaluate, the limit that would compute f'(x) (the formula for the derivative of f at any point) 3. Choose one of the limits you set up and evaluate it to find either f'(2) or f'(x). Note: Use of shortcut rules on this learning target is prohibited.

Learning Target D1: I can find the derivative of a function, both at a point and as a function, using the definition of the derivative. Consider the function f(x) 5x²+2x+5. 1. Set up, but do not evaluate, the limit that would compute f'(2) (the derivative of f at x = = 2) = 2. Set up, but do not evaluate, the limit that would compute f'(x) (the formula for the derivative of f at any point) 3. Choose one of the limits you set up and evaluate it to find either f'(2) or f'(x). Note: Use of shortcut rules on this learning target is prohibited.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

See similar textbooks

Similar questions

Using the limit definition of a derivative, evaluate the following derivatives. Use ofderivative shortcuts will result in no credit A)f (x)=10x-x^3 B)g(x)=x-2/x-3 C) y=SQRT(3T-1)
(a) Use Definition 5.2.1(Differentiability). to produce the proper formula for the derivative of h(x) = 1/x.
Using the limit definition of the derivative of a function at a point, show that the function f(x)= |x-2| is not differentiable at a=2.
Experiment 3: 3D. Does f'(0), the y-coordinate on the gray line at x = 0, have any relationship to the derivative value f'(0)? 3E. Does f'(0), the y-coordinate on the derivative line at x = 0, have any relationship to f(0), the y-coord. on the parabola at x = 0?
Find relative extrema of the function. Use the second derivative test when applicable. (If an answer does not exist, enter DNE). 1. f(x) = 15x^2 - x^3 Relative Maximum = ? Relative Minimum = ? 2. f(x) = x^4 + 4x^3 -1 Relative Maximum = ? Relative Minimum = ?
What is the defintion of a derivative? Usng the definition of a derivative at a given point, find the first derivative of the fuction z(x)= (-7x+1)1/2
Use the limit of defination of derivative. a) Find the slope of the curve y=1/x at any point x = a≠0. What is the slope at the point x= -1 ? b) Where does the slope equal -1/4? Show that with a sketch.
Compute the derivative function f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = 9x2 + x f '(x) =
Compute the derivative function f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = 7x2 + x
Part 1: Use the definition of the derviative to compute the derivative of f(x)=1−8x2f(x)=1−8x2 at the specific point x=2x=2. A) Evaluate the limit by using algebra to simplify the difference quotient and B) then evaluating the limit. Part 2: Use the definition of the derivative to compute the derivative of the function f(x)=1−8x2f(x)=1−8x2 at an arbitrary point x. A) Evaluate the limit by using algebra to simplify the difference quotient and B) then evaluating the limit. Part 3: Now let’s calculate the tangent line to the function f(x)=1−8x2f(x)=1−8x2 at x=4x=4. a) By using f′(x)f′(x) from part 2, the slope of the tangent line to f at x=4x=4 is f′(4)=f′(4)= . b) The tangent line to ff at x=4x=4 passes through the point (4,f(4))=(4,f(4))= [blank] on the graph of f. c) An equation for the tangent line to f at x=4x=4 is y=