f is the function whose graph is given below.

Question

https://ibb.co/4PZXp5v

see the image

Answer 1

The function g(x) is the area under the curve of f between 0 and x.

(a) Starting from 0, that area keeps increasing until x=2,

at which point the area starts decreasing.

Then at x=4 the area starts increasing again.

Therefore the local maxima and minima of g(x) are at x=2, x=4, x=6, x=8.

(b) The function g is concave down where its derivative, f, is decreasing.

That is on the intervals [1,3], [5,7], [9,8].