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Lilit [14]
3 years ago
5

I don’t understand this

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
3 0

Answer:

3 to the third power minus 3 and the product you add to 3/4 and simplify it

Step-by-step explanation:

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5929/x = x

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Hope this helps!

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68

Step-by-step explanation:

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].
castortr0y [4]

Answer:

The absolute maximum is \frac{3\sqrt 3}2 and the absolute minimum value is 0.

Step-by-step explanation:

Differentiate of f both sides w.r.t.  t,

f(t)=2 \cos t+\sin 2t

\Rightarrow f'(t)=-2\sin t+2\cos 2t

Now take f'(t)=0

\Rightarrow -2\sin t+2\cos 2t=0

\Rightarrow 2\cos 2t=2\sin t

\Rightarrow \cos 2t=\sin t

\Rightarrow 1-2\sin ^2t =\sin t  \quad \quad  [\because \cos 2t = 1-2\sin ^2t]

\Rightarrow 2\sin ^2t+\sin t-1=0

\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0

\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0

\Rightarrow (\sin t+1)(2\sin t-1)=0

\Rightarrow \sin t+1=0  \;\text{and}\; 2\sin t-1=0

\Rightarrow \sin t =-1  \;\text{and}\;   \sin t =\frac 12

In the interval 0\leq t\leq \frac {\pi}2, the answer to this problem is \frac {\pi}6

Now find the second derivative of f(t) w.r.t.   t,

f''(t)=-2\cos t-4\sin 2t

\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3

Thus, f(t) is maximum at t=\frac {\pi}6 and minimum at t=0

\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0

Hence, the absolute maximum is \frac{3\sqrt 3}2 and the absolute minimum value is 0.

7 0
3 years ago
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