Take the 2-minute tour ×
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.

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|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

2 Answers 2

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

share|improve this answer

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);

                      1.576726466

Plugging this into the second derivative we get...

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

                      -76.34072337
share|improve this answer

Your Answer

 
discard

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.