Question

use the alternative form of the derivative to find the derivative at x = c, if it exists. (if an answer does not exist, enter
f(x)=x^2 - 3, c = 6
f(6)=\lim_{x\to c}\frac{f(x)-f(c)}{x - c}
=\lim_{x\to 6}\frac{(x^2 - 3)-( )}{x-(6)}
= 12

Explanation:

Step1: Compute f(6)

$f(6) = 6^2 - 3 = 33$

Step2: Substitute into limit

$\lim_{x \to 6} \frac{(x^2 - 3) - 33}{x - 6} = \lim_{x \to 6} \frac{x^2 - 36}{x - 6}$

Step3: Factor numerator

$x^2 - 36 = (x - 6)(x + 6)$

Step4: Simplify and evaluate limit

$\lim_{x \to 6} (x + 6) = 6 + 6 = 12$

Answer:

12