Question

How do you find the equation of the line tangent to the graph of `F(x)=x^2+2x+1` at (-3,4)?

Answer 1

`y=-4x-8`

Explanation:

The gradient of the curve `F(x)=x^2+2x+1` is `F'(x)=2x+2`.

When `x=-3, F'(-3)=2(-3)+2=-4`

So, the gradient of the tangent to the curve `F(x)` at `x=-3` is `-4`.

The equation of the tangent is given by, `y-4=-4(x-(-3))`

`therefore y=-4x-8`