Calculus Problem

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March 8th 2006, 02:54 PM
frozenflames

Calculus Problem

Please see attached.

http://img225.imageshack.us/img225/1945/approb3ng.jpg
March 9th 2006, 05:21 AM
CaptainBlack

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

$<br /> g(-2)=\frac{f(1)+f(-2)}{2}\times (-3)=-6<br />$
March 9th 2006, 05:26 AM
CaptainBlack

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
March 9th 2006, 05:33 AM
CaptainBlack

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
March 9th 2006, 06:21 AM
CaptainBlack

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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