Please see attached.

http://img225.imageshack.us/img225/1945/approb3ng.jpg

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- Mar 8th 2006, 02:54 PMfrozenflamesCalculus Problem
Please see attached.

http://img225.imageshack.us/img225/1945/approb3ng.jpg - Mar 9th 2006, 05:21 AMCaptainBlack
a)

$\displaystyle

g(4)=\frac{f(1)+f(2)}{2}\times1+\frac{f(2)+f(4)}{2 }\times 2=2.5

$

$\displaystyle

g(-2)=\frac{f(1)+f(-2)}{2}\times (-3)=-6

$ - Mar 9th 2006, 05:26 AMCaptainBlack
b)

Form the fundamental theorem of calculus:

$\displaystyle

\frac{d}{dx} \int_a^x f(t)dt=f(x)

$,

so:

$\displaystyle

\frac{d}{dx} g|_{x=1}=f(1)=4

$.

RonL - Mar 9th 2006, 05:33 AMCaptainBlack
c)

$\displaystyle g(x)$ is increasing from $\displaystyle -6$ at $\displaystyle x=-2$ untill $\displaystyle x=3$ from where it

decreases to $\displaystyle 2.5$ at $\displaystyle x=4$.

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

RonL - Mar 9th 2006, 06:21 AMCaptainBlack
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