Let g(x)=x^2-2. The equation of the tangent line to the curve at (-1,-1) is 2x+y=-3.

Question

a. What is the slope of the tangent line to the curve at (-1,-1)?

b. What is the derivative of the function when x=-1?

Answer 1

Write the equation of the tangent line as y=-2x-3 and you will immediately see that the slope is -2 (for all x).

g'(x)=2x and at x=-1, g(-1)=-2.