Question

Help find the tangent line?

Answer 1

The function is f(x) = x² + 4x - 3

f(-3) = (-3)² + 4(-3) - 3 = -6

Let y = x² + 4x - 3

Apply derivative on each side with respect to x.

y' = 2x + 4

Slope of the tangent line at x = -3

y' = 2*(-3) + 4

y' = -2

m = -2

Tangent line at point (-3, f(-3))

f(-3) = -6

Tangent Line Equation is given as (y - y1) = m(x - x1).

(y - (-6)) = -2(x - (-3))

y + 6 = -2(x+3)

y + 6 = -2x - 6

y = -2x -12.

Graph

Therefore the tangent line equation is y = -2x -12.