Question

What is the equation of the line tangent to `f(x)=3x^2 - 2` at `x=4`?

Answer 1

Equation of tangent is `24x-y-50=0`

Explanation:

The slope of the tangent is given by the value of the derivative of the function `f(x)=3x^2-2` at `x=4`. As `f'(x)=6x` and at `x=4`, `f'(x)=6xx4=24`, slope of tangent at `x=4` is `24`.

At `x=4`, `f(x)=3xx4^2-2=46`, hence tangent passes through `(4,46)`.

Now using point slope form, equation of tangent is

`(y-46)=24(x-4)` or `y-46=24x-96` and

Equation of tangent is `24x-y-50=0`