What is the extreme f(x)=4sin(x)cos(x)+12 ?

The extreme f(x)=4sin(x)cos(x)+12 is Maximum(pi/4+pin,14),Minimum((3pi)/4+pin,10)

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extreme f(x)=4sin(x)cos(x)+12

extreme points

f (x) = 4 sin (x) cos (x) + 12

Maximum (\frac{π}{4} + πn, 14), Minimum (\frac{3 π}{4} + πn, 10)

Solution steps

Find the critical points:

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Domain of

4 sin (x) cos (x) + 12 : - \infty < x < \infty

Find intervals:

Increasing

: πn \leq x < \frac{π}{4} + πn,

Decreasing

: \frac{π}{4} + πn < x < \frac{3 π}{4} + πn,

Increasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

4 sin (x) cos (x) + 12 \Rightarrow y = 14

Maximum (\frac{π}{4} + πn, 14)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

4 sin (x) cos (x) + 12 \Rightarrow y = 10

Minimum (\frac{3 π}{4} + πn, 10)

Maximum (\frac{π}{4} + πn, 14), Minimum (\frac{3 π}{4} + πn, 10)

x (57 - x^{2})

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 7

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 6

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 1

Q (a, b) = 7 a (a - 2 b) + a (a - 3 b) + 2 a^{2} - 8 b^{2}

What is the extreme f(x)=4sin(x)cos(x)+12 ?
The extreme f(x)=4sin(x)cos(x)+12 is Maximum(pi/4+pin,14),Minimum((3pi)/4+pin,10)