Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given $$ f(x) = 5\sin\left(\frac14 x^4\right) -\sin\left(\frac12 x\right)^4 $$ Find, to 10 significant figures, the unique turning point of x[0] in the interval [1,2].

Also, I've got to get the second derivative in 10 significant figures.

The plot doesn't exactly make sense in maple, don't think I understand how to go about solving it mathematically.

original image here

share|cite|improve this question
Also, you will need the definition of "turning point" and the connection between $x$ and $\mathtt{x[0]}$. – GEdgar Sep 26 '12 at 17:30

If by "turning point" you mean relative extrema, then the only relative max on your interval is located at $x \approx 1.576726466$.

[> f := x -> 5*sin(x^4/4)-sin(x/2)^4;
[> plot(f(x),x=1..2);

plot of f(x)

Setting $f'(x)=0$ and solving we get...

[> x[0] := fsolve(diff(f(x),x)=0,x=1.6);


Plugging this into the second derivative we get...

[> evalf(subs(x=x[0],diff(f(x),x,x)));

share|cite|improve this answer

$\tt fsolve(diff(5*sin(x^4/4)-sin(x/2)^4, x\$2), x, 1 .. 2)$ gives 1.321411467.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.