What is the equation of the line tangent to f(x)=4x^2 + 4x - 4f(x)=4x2+4x4 at x=-2x=2?

1 Answer
Dec 20, 2015

y=-12x-20y=12x20

Explanation:

The tangent line will pass through the point (-2,f(-2))(2,f(2)).

f(-2)=4(-2)^2+4(-2)-4=4f(2)=4(2)2+4(2)4=4

Thus, the tangent line will pass through the point (-2,4)(2,4) and have a slope of f'(-2).

f'(x)=8x+4

f'(-2)=8(-2)+4=-12

The slope of the tangent line is -12 and it passes through (-2,4).

Write this in point-slope form.

y-4=-12(x+2)

In slope-intercept form:

y=-12x-20

graph{(y+12x+20)(4x^2+4x-4-y)=0 [-23.14, 17.41, -8.89, 11.37]}