Find the derivative by the limit process. f(x) = 15 – x²

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Tutorial Exercise
Find the derivative by the limit process.
f(x) = 15 – x²
Step 1
Complete the definition of a derivative. f (x) =
f(x + Ax) – f(x)
lim
Ax
Ax → 0
Step 2
Use the definition for the function above to find the derivative.
(x + Ax)² – (
x2)
f '(x) = lim
Ax-0
Ax
15 - x2 –
xAx - (Ax)² –
+ x2
lim
Ax-0
Ax
f '(x) =
xAx - (Ax)?
= lim
Ax-0
Ax
lim
Ax0
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Transcribed Image Text:Tutorial Exercise Find the derivative by the limit process. f(x) = 15 – x² Step 1 Complete the definition of a derivative. f (x) = f(x + Ax) – f(x) lim Ax Ax → 0 Step 2 Use the definition for the function above to find the derivative. (x + Ax)² – ( x2) f '(x) = lim Ax-0 Ax 15 - x2 – xAx - (Ax)² – + x2 lim Ax-0 Ax f '(x) = xAx - (Ax)? = lim Ax-0 Ax lim Ax0 Submit Skip (you cannot come back) Viewing Saved Work Revert to Last Response Submit Answer Question 1 of 5 View Next Ques
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