Question

What are the critical values, if any, of `f(x)=2x^3 - 54x^2 + 480x - 1300`?

Answer 1

Start by finding the derivative.

`f'(x) = 6x^2 - 108x + 480`

`f'(x) = 6(x^2 - 18x + 80)`

`f'(x) = 6(x - 10)(x - 8)`

The critical values occur when `f'(x) = 0` or is undefined.

There will be no undefined points in this function, so we set this to `0` and solve.

`0 = 6(x - 10)(x - 8)`

`x = 10 and 8`

Therefore, the critical values are `x = 10` and `x = 8`.