Question

Question #c6955

Answer 1

`"SP": (1/3sqrt 2, 4/9sqrt2), (-1/3sqrt2, -4/9sqrt2)`

Explanation:

`f(x) = 2x-3x^3`

In order to find the stationary points if this function, we need to find `f'` and solve it for `x`.

`f'= 2-9x^2`

Let `f' = 0`

Then `2-9x^2 = 0`

`9x^2=2`

`x^2=2/9`

`x= +-sqrt2/3`

We have found the `x`-coordinates of the stationary points and we know need to find the `y`-coordinates.

`f(sqrt2/3) = 4/9sqrt2`

`f(-sqrt2/3) = -4/9sqrt2`

So the SP are `(1"/"3sqrt2, 4"/"9sqrt2) and (-1"/"sqrt2, -4"/"9sqrt2)`.