What is the extreme y=32cos(10x)+25 ?

The extreme y=32cos(10x)+25 is Maximum(pi/5 n,57),Minimum(pi/(10)+pi/5 n,-7)

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extreme y=32cos(10x)+25

extreme points

y = 32 cos (10 x) + 25

Maximum (\frac{π}{5} n, 57), Minimum (\frac{π}{10} + \frac{π}{5} n, - 7)

Solution steps

Find the critical points:

x = \frac{π}{5} n, x = \frac{π}{10} + \frac{π}{5} n

Domain of

32 cos (10 x) + 25 : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{π}{5} n < x < \frac{π}{10} + \frac{π}{5} n,

Increasing

: \frac{π}{10} + \frac{π}{5} n < x < \frac{π}{5} + \frac{π}{5} n

Plug the extreme point

x = \frac{π}{5} n

into

32 cos (10 x) + 25 \Rightarrow y = 57

Maximum (\frac{π}{5} n, 57)

Plug the extreme point

x = \frac{π}{10} + \frac{π}{5} n

into

32 cos (10 x) + 25 \Rightarrow y = - 7

Minimum (\frac{π}{10} + \frac{π}{5} n, - 7)

Maximum (\frac{π}{5} n, 57), Minimum (\frac{π}{10} + \frac{π}{5} n, - 7)

f (x) = - 2 x^{2} + 4

\frac{1 - 2 x}{x ^{2} - x}

x^{4} + x^{3} - 8 x^{2} - 12 x

f (x) = e^{x} (x - 9)

3 x^{2} + 2 x [- 2.1]

What is the extreme y=32cos(10x)+25 ?
The extreme y=32cos(10x)+25 is Maximum(pi/5 n,57),Minimum(pi/(10)+pi/5 n,-7)