For what value of x does 6 sin (2x - 25)^o attain its maximum value in the range 0^o \(\leq\) x \(\leq\) 180^o

12\(\frac{1}{2}\)

32\(\frac{1}{2}\)

57\(\frac{1}{2}\)

147\(\frac{1}{2}\)

Correct answer is C

y = 6 sin (2x - 25)^o

\(\frac{dy}{dx}\) = -12 cos(2x - 25^o)

\(\frac{dy}{dx}\) = 0

-12 cos x (2x - 25^o) = 0

= cos(2x - 25^o) = 0

= 2x - 25^o = cos^-1(0)

= 2x - 25^o

= 90^o

x = \(\frac{115}{2}\)

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For what value of x does 6 sin (2x - 25)o attain its maximum value in the range 0o \(\leq\) x \(\leq\) 180o

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For what value of x does 6 sin (2x - 25)^o attain its maximum value in the range 0^o \(\leq\) x \(\leq\) 180^o