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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    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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  2. UnkleRhaukus
    • one year ago
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    at what point on the x-axis, do the infinitesimal 'areas' under the curve stop being positive, and start being negative ?

  3. anonymous
    • one year ago
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    from x=5 to x=7

  4. UnkleRhaukus
    • one year ago
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    yeah, all the infinitesimal 'areas' between x=5&7 are negative, whereas the the 'areas' between x=1&5 are positive

  5. UnkleRhaukus
    • one year ago
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    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

  6. UnkleRhaukus
    • one year ago
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    the largest integral we can get is when we are only add positive values

  7. UnkleRhaukus
    • one year ago
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    . So, (where g(x) is the integral from 1to x) For what value of x does g(x) have a maximum?

  8. anonymous
    • one year ago
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    so we would only look at the positive values (x=1 to 5) ?

  9. UnkleRhaukus
    • one year ago
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    yeah, the lower limit of integration is given as x = 1, and as you have found the upper limit of integration is x = 5

  10. UnkleRhaukus
    • one year ago
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    That's right

  11. anonymous
    • one year ago
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    thank you!

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