Question

How do you find the equation of the line tangent to the graph of `f(x)=x^4` at x=-1?

Answer 1

`y=-4x-5`

Explanation:

`f(x)=x ^4`
`f'(x)=4x^3`

`f'` ,the first derivative, is the gradient function, and gives the gradient at any point on the curve.
So at the point when `x` is -1 the gradient is -4 because
`4*(-1)^3`=-4

So the equation of the tangent is `y=-4x+c`

We also know that at the point on the curve where x =--1, y=1
This point is on the tangent.

1=-4+c gives c=-5
Now sketch the curve and you will see that it makes sense