Question

Compute f '(a) algebraically for the given value of a.
f(x) = x2 − 5; a = 3

Answer 1

f'(x) = 2*x
f'(3) = 2*3 = 6

Answer 2

f(x) = x2 − 5
Apply Derivative Formula
f'(x)=2x
f'(a)=2a
a=3
f'(3)=2*3
f'(3)=6

Answer 3

@Ashleyisakitty Do you understand how to differentiate (find the derivative)?

Answer 4

\[
f'(a) = \lim_{x\to a}\frac{f(x)-f(a)}{x-a}= \lim_{x\to a}\frac{(x^2-5)-(a^2-5)}{x-a}
\]

Answer 5

\[
\lim_{x\to a}\frac{x^2-a^2}{x-a} = \lim_{x\to a}\frac{(x-a)(x+a)}{x-a}=\lim_{x\to a}x+a = a+a = 2a
\]

Answer 6

So since \[
f'(a) = 2a
\]And \(a=3\), we get \[
f'(3) = 2(3)=6
\]Just as the others have said.