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Derivative of Standard Functions

10.The values...

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10.The values of x for which function f(x)= cos(2x+pi/4) is decreasing are a) (-pi/8,pi/8)

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Q. Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8).

Q. Show that the function

f (x) = sin (2 x + π / 4)

is decreasing on

(3 π / 8, 5 π / 8)

Q. The function

f (x) = sin 2 x + cos 2 x \forall x \in [0, \frac{π}{2}]

is strictly decreasing in the interval

Q. The value of

{sin}^{4} \frac{π}{8} + {sin}^{4} \frac{3 π}{8} + {sin}^{4} \frac{5 π}{8} + {sin}^{4} \frac{7 π}{8}

g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2

f : [\frac{π}{8}, \frac{3 π}{8}] \to R

be functions such that

g_{1} (x) = 1, g_{2} (x) = | 4 x - π |

f (x) = {sin}^{2} x,

x \in [\frac{π}{8}, \frac{3 π}{8}] .

S_{i} = 3 π / 8 \int π / 8 f (x) \cdot g_{i} (x) d x, i = 1, 2,

then the value of

\frac{16 S_{1}}{π}

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