What is the slope of the line normal to the tangent line of f(x) = x^2e^(x-1)+2x-2 at x= 1 ?

1 Answer
Jul 18, 2018

-1/4

Explanation:

We know that a normal line is orthogonal to a tangent line, so we should find the slope of the tangent line first, then find the slope orthogonal to it.

The slope of the tangent line is just the derivative:
f'(x) = 2x e^(x-1) + x^2 e^(x-1) + 2
f'(1) = 2e^0 + 1e^0 + 2 = 4

Two orthogonal lines have
m_1m_2 = -1

so
m_(norm) * 4 = -1 implies m_(norm) = -1/4