Question

1. if the line tangent to the graph of the function f at the point (3,6) passes through the point (-2, -4), then f(3) =

Explanation:

Step1: Recall derivative as slope

The value $f'(3)$ is the slope of the tangent line to $f$ at $(3,6)$.

Step2: Use slope formula

Calculate slope between $(3,6)$ and $(-2,-4)$:
$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 6}{-2 - 3}$

Step3: Simplify the expression

$\frac{-10}{-5} = 2$

Answer:

$2$