It's a calculus problem?

enter image source here

1 Answer
Sep 22, 2017

f has 3 relative maxima, 2 relative minima, and 6 points of inflexion at which the tangents are not horizontal.

Explanation:

  • At a local maximum, the derivative will transition from positive to negative. We see 3 examples where f' intersects the x axis, changing from positive to negative. So there are 3 local maxima.

  • At a local minimum, the derivative will transition from negative to positive. We see 2 examples where f' intersects the x axis, changing from negative to positive. So there are 2 local minima.

  • At a point of inflexion where the tangent is not horizontal, the derivative f' has a local maximum or minimum but does not touch the x axis. There are 6 examples of that in the given graph of f'.

So f has 3 relative maxima, 2 relative minima, and 6 points of inflexion at which the tangents are not horizontal.