Question

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)?

Answer 1

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`