# Thread: find f given f"

1. ## find f given f"

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

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

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

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

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

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

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

$\displaystyle f(4)=\frac{128}{3} +D=\frac{330}{10}$
$\displaystyle D=\frac{202}{3}$

I got this, but it was wrong:$\displaystyle f(t)=$

2. Originally Posted by hazecraze
Find f. f ''(t) = 4/√t
f(4) = 22
f '(4) = 5

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

so f'= $\displaystyle f'=8\bold{\color{red}t}^{1/2} -11$
...
$\displaystyle f'(t)=8t^{\frac12}-11$
2. $\displaystyle f(t)=\frac23 \cdot 8 t^{\frac32} - 11t + c$
I've got $\displaystyle c = \frac{166}3$