What is the extreme f(x)=32sin(pi/3 x)+42 ?

The extreme f(x)=32sin(pi/3 x)+42 is Maximum(3/2+6n,74),Minimum(9/2+6n,10)

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extreme f(x)=32sin(pi/3 x)+42

extreme points

f (x) = 32 sin (\frac{π}{3} x) + 42

Maximum (\frac{3}{2} + 6 n, 74), Minimum (\frac{9}{2} + 6 n, 10)

Solution steps

Find the critical points:

x = \frac{3}{2} + 6 n, x = \frac{9}{2} + 6 n

Domain of

32 sin (\frac{π}{3} x) + 42 : - \infty < x < \infty

Find intervals:

Increasing

: 6 n \leq x < \frac{3}{2} + 6 n,

Decreasing

: \frac{3}{2} + 6 n < x < \frac{9}{2} + 6 n,

Increasing

: \frac{9}{2} + 6 n < x < 6 + 6 n

Plug the extreme point

x = \frac{3}{2} + 6 n

into

32 sin (\frac{π}{3} x) + 42 \Rightarrow y = 74

Maximum (\frac{3}{2} + 6 n, 74)

Plug the extreme point

x = \frac{9}{2} + 6 n

into

32 sin (\frac{π}{3} x) + 42 \Rightarrow y = 10

Minimum (\frac{9}{2} + 6 n, 10)

Maximum (\frac{3}{2} + 6 n, 74), Minimum (\frac{9}{2} + 6 n, 10)

f (x) = 2 - x^{\frac{2}{5}}

f (x) = - 6 x + e^{x}

f (x, y) = x^{2} + y^{2} - 2 y

14 x^{2} - 2 x^{3} + 4 x y

f (x) = x^{4} + x^{3}

What is the extreme f(x)=32sin(pi/3 x)+42 ?
The extreme f(x)=32sin(pi/3 x)+42 is Maximum(3/2+6n,74),Minimum(9/2+6n,10)