Question

What is the equation of the line tangent to `f(x)=3x^2-2x-5` at `x=-2`?

Answer 1

`y-11=-14(x+2)`

Explanation:

`f(x)=3x^2-2x-5`
`f'(x)=6x-2`

`f(-2)=11`
`f'(-2)=-14`

Thus, the tangent line will intersect `f` at `(-2,11)` and will have a slope of `-14`.

Write the equation in point slope form:

`y-11=-14(x+2)`