find f given f"

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November 28th 2009, 10:33 AM
hazecraze

find f given f"

Find f. f ''(t) = 4/√t
f(4) = 22
f '(4) = 5

$f"= 4t^{-1/2}$
$f'=2(4)t^{1/2} +C$
$f'(4)=16+C=5$
$C=-11$

so f'= $f'=8^{1/2} -11t$
$f=(2)\frac{8t^{3/2}}{3} -\frac{11t^2}{2}+D$

$f(4)=(2)\frac{8(4)^{3/2}}{3} -\frac{11(4)^2}{2}+D=22$

$f(4)=\frac{16(8)}{3} -\frac{11(16)}{2}+D=22$

$f(4)=\frac{128}{3} -88+D=22$

$f(4)=\frac{128}{3} +D=110$

$f(4)=\frac{128}{3} +D=\frac{330}{10}$
$<br /> D=\frac{202}{3}$

I got this, but it was wrong: $f(t)=$ http://www.webassign.net/cgi-bin/pal...E%3C%2Fmath%3E
November 28th 2009, 11:29 AM
earboth

Quote:

Originally Posted by hazecraze

Find f. f ''(t) = 4/√t
f(4) = 22
f '(4) = 5

$f"= 4t^{-1/2}$
$f'=2(4)t^{1/2} +C$
$f'(4)=16+C=5$
$C=-11$ <<<<<< OK

so f'= $f'=8\bold{\color{red}t}^{1/2} -11$
...

1. According to your calculations:

$f'(t)=8t^{\frac12}-11$

2. $f(t)=\frac23 \cdot 8 t^{\frac32} - 11t + c$

3. Now f(4) = 22

Plug in this value to calculate c.

I've got $c = \frac{166}3$

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