Question

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

Answer 1

The tangent line is `y = 8x - 9`

Explanation:

Differentiate the equation to find the gradient.
`f'(x) = 2x +2`

At the point `x = 3` this equals `8` which is the gradient.

The equation for the tangent is `y = mx + c` where `m` is the gradient and `c` is the y-intercept.

We can find `c` by using the coordinates of the specified point.

At `x=3` , `y = 3^2 +2*3 =15`

This point is also on the tangent line, so we can say `15 = 8*3 + c`
Therefore `c = 15 - 24 = -9`

The tangent line is `y = 8x - 9`