Question

1. (15 points) find the equation of the tangent line to the curve $y = 4x - x^2$ at $(1, 3)$. also find the slope intercept.

Explanation:

Step1: Compute derivative of y

$y' = 4 - 2x$

Step2: Find slope at x=1

$m = 4 - 2(1) = 2$

Step3: Use point-slope form

$y - 3 = 2(x - 1)$

Step4: Convert to slope-intercept

$y = 2x + 1$

Answer:

Equation of tangent line: $y = 2x + 1$; Slope intercept: 1