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Math Help - Calculus Problem

  1. #1
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    Calculus Problem

    Please see attached.

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  2. #2
    Grand Panjandrum
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    a)
    <br />
g(4)=\frac{f(1)+f(2)}{2}\times1+\frac{f(2)+f(4)}{2  }\times 2=2.5<br />

    <br />
g(-2)=\frac{f(1)+f(-2)}{2}\times (-3)=-6<br />
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  3. #3
    Grand Panjandrum
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    b)

    Form the fundamental theorem of calculus:

    <br />
\frac{d}{dx} \int_a^x f(t)dt=f(x)<br />
,

    so:

    <br />
\frac{d}{dx} g|_{x=1}=f(1)=4<br />
.

    RonL
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  4. #4
    Grand Panjandrum
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    c)

    g(x) is increasing from -6 at x=-2 untill x=3 from where it
    decreases to 2.5 at x=4.

    Hence the mininmum of g is -6 which occures when x=-2

    RonL
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  5. #5
    Grand Panjandrum
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    d)

    x=1 is the only point of inflection the second derivative is positive to the
    left of the point and negative to the right. At no other point is there a
    change of sign of the second derivative and so there are no other points
    of inflection.

    RonL
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