what-is-maximum-value-of-y-3x-4-2-sin-2x-

Question Number 77574 by jagoll last updated on 08/Jan/20

w h a t i s m a x i m u m

v a l u e o f y = {(3 x + 4)}^{2} \times \sin (2 x)

Commented by MJS last updated on 08/Jan/20

\sin 2 x = - 1 \Rightarrow x = n π - \frac{π}{4} = \frac{4 n - 1}{4} π

\sin 2 x = + 1 \Rightarrow x = n π + \frac{π}{4} = \frac{4 n + 1}{4} π

n \in Z

f (x) = {(3 x + 4)}^{2} \sin 2 x

f (\frac{4 n - 1}{4} π) = - \frac{{(12 π n - 3 π + 16)}^{2}}{16}

n = \pm 10^{3} \Rightarrow f (x) \approx - 8.9 \times 10^{7}

n = \pm 10^{6} \Rightarrow f (x) \approx - 8.9 \times 10^{13}

n = \pm 10^{9} \Rightarrow f (x) \approx - 8.9 \times 10^{19}

\dots

Commented by jagoll last updated on 08/Jan/20

p l e a s e

Commented by MJS last updated on 08/Jan/20

no maximum because \lim_{x \to \pm \infty} {(3 x + 4)}^{2} = + \infty

Commented by jagoll last updated on 08/Jan/20

i f m i n i m u m s i r ?

Commented by MJS last updated on 08/Jan/20

also no minimum

- 1 ⩽ \sin 2 x ⩽ 1

- \infty < {(3 x + 4)}^{2} \sin 2 x < + \infty

Commented by jagoll last updated on 08/Jan/20

t h a n k s y o u s i r

Commented by jagoll last updated on 08/Jan/20

s i r m i n i m u m {(3 x + 4)}^{2} = 0

w h y m i n i m u m {(3 x + 4)}^{2} \times \sin (2 x) = - \infty

Commented by MJS last updated on 08/Jan/20

\dots similar for

f (\frac{4 n + 1}{4} π) = \frac{{(12 π n + 3 π + 16)}^{2}}{16}

Commented by jagoll last updated on 08/Jan/20

t h a n k s y o u s i r

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