# maximum value at given interval

• February 22nd 2010, 10:16 AM
bigwave
maximum value at given interval
$
f(x)=\sqrt{1+x^3}$

find the maximum value of |f''(x)| on the given Interval of $[0,2]$

calculated $f''(x)$ to be

$
f''(x) = \frac{3x(x^3+4)}{4(x^3+1)^{3/2}}$

thot setting this to zero would give where the maximum value is

but the answer is $f''|(\sqrt[3]{-10+\sqrt{108}})|=1.47$

graphing this can see that the top of the graph is 1.47 but don't see how this was derived.
• February 22nd 2010, 11:13 AM
Keithfert488
To find the max of f''(x) you have to set it's derivative (f'''(x)) to zero
• February 22nd 2010, 12:06 PM
bigwave
i did try this but did not get the answer as expected.
f'''(x) is pretty complicated.