Please answer only option c. I’ll also write the results of option a and b and upload the formula in option a. You can use them if you need.f’(0) = 4f’(1) = 2f’(2) = 0f’(3) = -2f’(4) = -4f’(5) = -6f’(a) = 2(2-a) (formula in option b) So lution :-%3DThisishsoderivative.limitde fini tion fthe Preview Activity 1.4.1. Consider the function f(x) = 4x – x².a. Use the limit definition to compute the derivative values: f'(0), f'(1), f'(2), andf'(3).b. Observe that the work to find f'(a) is the same, regardless of the value of a.Based on your work in (a), what do you conjecture is the value of f'(4)? Howabout f'(5)? (Note: you should not use the limit definition of the derivative tofind either value.)c. Conjecture a formula for f'(a) that depends only on the value a. That is, in thesame way that we have a formula for f(x) (recall f(x) = 4x – x²), see if you canuse your work above to guess a formula for f'(a) in terms of a.

Given that, fx=4x-x2 We need to compute the value of f'a.

Conjecture a formula for f'(a) that depends only on the value a. That is, in the same way that we have a formula for f(x) (recall f(x) = 4x - x2), see if you can use your work above to guess a formula for f'(a) in terms of a.

Conjecture a formula for f'(a) that depends only on the value a. That is, in the same way that we have a formula for f(x) (recall f(x) = 4x - x2), see if you can use your work above to guess a formula for f'(a) in terms of a.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Please answer only option c. I’ll also write the results of option a and b and upload the formula in option a. You can use them if you need. f’(0) = 4 f’(1) = 2 f’(2) = 0 f’(3) = -2 f’(4) = -4 f’(5) = -6 f’(a) = 2(2-a) (formula in option b)

So lution :-
%3D
This
is
hso
derivative.
limit
de fini tion f
the

Preview Activity 1.4.1. Consider the function f(x) = 4x – x².
a. Use the limit definition to compute the derivative values: f'(0), f'(1), f'(2), and
f'(3).
b. Observe that the work to find f'(a) is the same, regardless of the value of a.
Based on your work in (a), what do you conjecture is the value of f'(4)? How
about f'(5)? (Note: you should not use the limit definition of the derivative to
find either value.)
c. Conjecture a formula for f'(a) that depends only on the value a. That is, in the
same way that we have a formula for f(x) (recall f(x) = 4x – x²), see if you can
use your work above to guess a formula for f'(a) in terms of a.

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