How do you use the limit definition to find the slope of the tangent line to the graph -5x^2+8x+2 at (-1,-11)?

1 Answer
Jan 8, 2016

Use lim/(h->0) (f(x+h)-f(x))/h but before you complete any algebra, substitute -1 in for x, then simplify.

Explanation:

Here's the work:
lim/(h->0) (f(x+h)-f(x))/h
lim/(h->0) (f(-1+h)-f(-1))/h
lim/(h->0) (-5*(-1+h)^2+8(-1+h)+2-(-11))/h
lim/(h->0) (-5+10h-5h^2-8+8h+13)/h
lim/(h->0) (-5h^2+18h-13+13)/h
lim/(h->0) (h(-5h+18))/h
lim/(h->0) (-5h+18)
answer is 18