Question

. There are no local maximum or minimum values on the graph of A(x). Using the graph of y = R(t), explain why this is true.

Answer 1

I can't understand why not? There seems to be a maximum at t=50

Answer 2

A(x) is not R(t), is it?

Answer 3

No, sorry. It is the integral

Answer 4

The integral of R(t) has a derivative given by R(t). If R(t) is never 0, there are not local maxima or minima.

Answer 5

but the derivative of R(t) has a zero?

Answer 6

Sure, but if A(x) is the integral of R(t) from 0 to x and R(t) is always positive, A(t) will always be increasing.

Answer 7

Ok, this makes sense. Thanks for your time :)