Question

Find the minimum and maximum values of y=sqrt(14theta)-sqrt(7)sectheta on the interval [0, pi/3]

Answer 1

i got -sqrt(7) for f min but i can't get f max

Answer 2

\[y(\theta)=\sqrt{14\theta}-\sqrt7\sec\theta~~\implies~~\frac{dy}{d\theta}=\frac{7}{\sqrt{14\theta}}-\sqrt7\sec\theta\tan\theta\]
Solving for critical points:
\[\frac{7}{\sqrt{14\theta}}-\sqrt7\sec\theta\tan\theta=0\]
There's not much that can be done by hand, unfortunately. To find the solution for \(\theta\) you'll need to use a calculator: http://www.wolframalpha.com/input/?i=FindRoot%5BSqrt%5B7%2F2%5D%2FSqrt%5Bt%5D+-+Sqrt%5B7%5D+Sec%5Bt%5D+Tan%5Bt%5D%2C+%7Bt%2C+1%7D%5D

Answer 3

so are you supposed to plug in .6264721?

Answer 4

Keep in mind that the derivative knows nothing of endpoints. You must evaluate those separately.