anonymous
  • anonymous
g(x)= integral from 1 to x f(t) dt. for what value of x does g(x) have a maximum?
Mathematics
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katieb
  • katieb
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anonymous
  • anonymous
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?
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UnkleRhaukus
  • UnkleRhaukus
at what point on the x-axis, do the infinitesimal 'areas' under the curve stop being positive, and start being negative ?
anonymous
  • anonymous
from x=5 to x=7

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UnkleRhaukus
  • UnkleRhaukus
yeah, all the infinitesimal 'areas' between x=5&7 are negative, whereas the the 'areas' between x=1&5 are positive
UnkleRhaukus
  • UnkleRhaukus
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
UnkleRhaukus
  • UnkleRhaukus
the largest integral we can get is when we are only add positive values
UnkleRhaukus
  • UnkleRhaukus
. So, (where g(x) is the integral from 1to x) For what value of x does g(x) have a maximum?
anonymous
  • anonymous
so we would only look at the positive values (x=1 to 5) ?
UnkleRhaukus
  • UnkleRhaukus
yeah, the lower limit of integration is given as x = 1, and as you have found the upper limit of integration is x = 5
UnkleRhaukus
  • UnkleRhaukus
That's right
anonymous
  • anonymous
thank you!

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