CPM Homework Help : CALC3RD Problem 1-174

A focus of this course will be determining maximum and minimum values of a function on a given interval. However, you already have the skills to do this for certain functions. On your paper, sketch $y = 2 \sin(3x)$ for $\frac { 2 \pi } { 3 }$ . Determine the points at which the function is a maximum and a minimum.

Hint:

See graph at right.

$\text{It is a sine curve with amplitude 2 and period }\frac{2\pi}{3}.$

More Help:

The graph is a sine curve that is vertically stretched by a factor of $2$ and horizontally compressed by a factor of $3$ .

Periodic curve, x axis scaled from 0 to 2 thirds pi, with 3 equally spaced tick marks, starting at the origin, rising to 2 at the first tick mark, passing through the x axis at the second tick mark, falling to negative 2 at the third tick mark & returning to the x axis at 2 thirds pi.

Answer:

$\text{Maximum at } \left(\frac{\pi}{6},?\right), \text{ minimum at } (?,-2).$