What is the extreme-4sin(2pix) ?

The extreme-4sin(2pix) is Minimum(1/4+1*n,-4),Maximum(3/4+1*n,4)

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extreme-4sin(2pix)

extreme points

- 4 sin (2 π x)

Minimum (\frac{1}{4} + 1 \cdot n, - 4), Maximum (\frac{3}{4} + 1 \cdot n, 4)

Solution steps

Find the critical points:

x = \frac{1}{4} + 1 \cdot n, x = \frac{3}{4} + 1 \cdot n

Domain of

- 4 sin (2 π x) : - \infty < x < \infty

Find intervals:

Decreasing

: 1 \cdot n \leq x < \frac{1}{4} + 1 \cdot n,

Increasing

: \frac{1}{4} + 1 \cdot n < x < \frac{3}{4} + 1 \cdot n,

Decreasing

: \frac{3}{4} + 1 \cdot n < x < 1 + 1 \cdot n

Plug the extreme point

x = \frac{1}{4} + 1 n

into

- 4 sin (2 π x) \Rightarrow y = - 4

Minimum (\frac{1}{4} + 1 \cdot n, - 4)

Plug the extreme point

x = \frac{3}{4} + 1 n

into

- 4 sin (2 π x) \Rightarrow y = 4

Maximum (\frac{3}{4} + 1 \cdot n, 4)

Minimum (\frac{1}{4} + 1 \cdot n, - 4), Maximum (\frac{3}{4} + 1 \cdot n, 4)

f (x) = 20 + 8 x^{3} - x^{4}

f (x) = - 2 x^{3} + 15 x^{2} - 24 x, 0 \leq x \leq 5

\frac{e ^{x}}{6 + e ^{x}}

f (x, y) = 3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} - 2

f (x, y) = 4 x^{2} + 2 y^{2} + 6 x + 8 y + 2

What is the extreme-4sin(2pix) ?
The extreme-4sin(2pix) is Minimum(1/4+1*n,-4),Maximum(3/4+1*n,4)