Derivatives and Curves [Updated]

Complete the following question for tomorrow’s lesson.

Use the derivative of the function \[f(x)=x^3-x^2+2x-1\] to find the coordinates of the (local) extrema of \(f\).

Update: Oops! The function above has no extrema! (How can you tell from the first derivative?) However, it does have what’s called a point of inflexion, which is a point at which the function changes concavity (from concave up to concave down, or vice versa). Can you find the coordinates of the point of inflexion?

At any rate, the function \(g\) below does have extrema, so you should find the coordinates of the extrema of \(g\). Can you also find the coordinates of its point of inflexion?