Need help with point of inflection question

So I’ve just marked this question based on the mark scheme, and I understand why f’’(7) = 0, but would f’(7) = 0 not also be true? Because the gradient should equal zero when there’s a point of inflection?

(edited 8 months ago)

Reply 1

mqb2766

Original post

by College student2

No, a stationary point is f'(x)=0. A point of inflection is f''(x)=0. While a point can be both a stationary point and a point of inflection, in general theyre different.

Reply 2

College student2

Original post

by mqb2766

No, a stationary point is f'(x)=0. A point of inflection is f''(x)=0. While a point can be both a stationary point and a point of inflection, in general theyre different.

Thanks

Reply 3

mqb2766

Original post

by College student2

Thanks

Its worth having a pic in your head rather than just a defn so sketch/plot in desmos
f(x) = x^3
f(x) = x^3+x
and what do you notice about the x=0 point?