What is the extreme 15sin(5000pit) ?

The extreme 15sin(5000pit) is Maximum(1/10000+1/2500 n,15),Minimum(3/10000+1/2500 n,-15)

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extreme 15sin(5000pit)

extreme points

15 sin (5000 π t)

Maximum (\frac{1}{10000} + \frac{1}{2500} n, 15), Minimum (\frac{3}{10000} + \frac{1}{2500} n, - 15)

Solution steps

Find the critical points:

t = \frac{1}{10000} + \frac{1}{2500} n, t = \frac{3}{10000} + \frac{1}{2500} n

Domain of

15 sin (5000 π t) : - \infty < t < \infty

Find intervals:

Increasing

: \frac{1}{2500} n \leq t < \frac{1}{10000} + \frac{1}{2500} n,

Decreasing

: \frac{1}{10000} + \frac{1}{2500} n < t < \frac{3}{10000} + \frac{1}{2500} n,

Increasing

: \frac{3}{10000} + \frac{1}{2500} n < t < \frac{1}{2500} + \frac{1}{2500} n

Plug the extreme point

x = \frac{1}{10000} + \frac{1}{2500} n

into

15 sin (5000 π t) \Rightarrow y = 15

Maximum (\frac{1}{10000} + \frac{1}{2500} n, 15)

Plug the extreme point

x = \frac{3}{10000} + \frac{1}{2500} n

into

15 sin (5000 π t) \Rightarrow y = - 15

Minimum (\frac{3}{10000} + \frac{1}{2500} n, - 15)

Maximum (\frac{1}{10000} + \frac{1}{2500} n, 15), Minimum (\frac{3}{10000} + \frac{1}{2500} n, - 15)

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

f (x) = 9 \cdot x^{3} - 7 \cdot x^{2} + 3 \cdot x + 10

f (x) = x^{2} - 6, - 2 \leq x \leq 4

f (x, y) = e^{- 2 x^{2} - 4 y^{2}}

6 x^{2} - 48 x - 190

What is the extreme 15sin(5000pit) ?
The extreme 15sin(5000pit) is Maximum(1/10000+1/2500 n,15),Minimum(3/10000+1/2500 n,-15)