Question

Find equation of the tangent line f(x)=x^2 at (-2, 4)?

Answer 1

`y=-4x-4`

Explanation:

First, we need to find the slope to the tangent line to the curve provided by `f(x)=x^2` at `x=-2.`

Recall that graphically interpreted, the derivative provides the rate of change of the function at a point, or, the slope of the tangent line to the curve at a point.

Differentiate:

`f'(x)=2x`

Determine the derivative at `x=-2:`

`f'(-2)=2(-2)=-4`

Now, to find the equation, we use the point-slope form of a line:

`y-y_0=m(x-x_0)` where `m` is the slope, `(x_0,y_0)=(-2,4)`

`y-4=-4(x+2)`

`y-4=-4x-8`

`y=-4x-4`