It's a calculus problem?
1 Answer
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