Question

g(x)= integral from 1 to x f(t) dt. for what value of x does g(x) have a maximum?

Answer 1

The graph of f is shown in the figure. g(x)= integral from 1 to x f(t) dt. for what value of x does g(x) have a maximum?

Answer 2

at what point on the x-axis, do the infinitesimal 'areas' under the curve stop being positive, and start being negative ?

Answer 3

from x=5 to x=7

Answer 4

yeah, all the infinitesimal 'areas' between x=5&7 are negative,
whereas the the 'areas' between x=1&5 are positive

Answer 5

if we integrated all the way from x=1 to x=7,

we would get what is equal to PLUS the area from1to5, MINUS the area from5to7

Answer 6

the largest integral we can get is when we are only add positive values

Answer 7

.

So, (where g(x) is the integral from 1to x)
For what value of x does g(x) have a maximum?

Answer 8

so we would only look at the positive values (x=1 to 5) ?

Answer 9

yeah,
the lower limit of integration is given as x = 1,
and as you have found the upper limit of integration is x = 5

Answer 10

That's right

Answer 11

thank you!