# Math Help - maximum value at given interval

1. ## 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.

2. To find the max of f''(x) you have to set it's derivative (f'''(x)) to zero

3. i did try this but did not get the answer as expected.
f'''(x) is pretty complicated.