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Algebra> At what point in the interval [0,2?] does...

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At what point in the interval [0,2?] does the function Sin2x attain its maximum value?

Manvendra Singh chahar , 12 Years ago

Grade Upto college level

1 Answers

Jitender Singh

Ans:

$f(x) = sin(2x)$

$f^{'}(x) = 2cos(2x) = 0$

$2x = (n + \frac{1}{2})\pi$

$x = (n + \frac{1}{2})\frac{\pi }{2}$

$x = \frac{\pi }{4}, \frac{3\pi }{4}, \frac{5\pi }{4}, \frac{7\pi }{4}$

$f^{''}(x) = -4sin(2x)$

$f^{''}(\frac{\pi }{4}) = -4sin(2.\frac{\pi }{4}) = -4$

$f^{''}(\frac{3\pi }{4}) = -4sin(2.\frac{3\pi }{4}) = 4$

$f^{''}(\frac{5\pi }{4}) = -4sin(2.\frac{5\pi }{4}) = -4$

$f^{''}(\frac{7\pi }{4}) = -4sin(2.\frac{7\pi }{4}) = 4$

$x = \frac{\pi }{4}, \frac{5\pi }{4}$

is the pont of maxima.

Thanks & Regards

Jitender Singh

IIT Delhi

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