Answer to Question #179873 in Physics for Johannes Steven

Question

Let f(x) = 1/3x³ + x² - 15x - 9. Use detailed sign tables in answering the following questions

(a) Find the intervals in which f is increasing or decreasing.

(b) Find the intervals in which the graph of y = f(x) is concave upwards or downwards.

Air is escaping from a spherical balloon at the rate of 2 cm³ per minute. How fast is the radius shrinking when the volume is 36 pi cm³.

Find the rate of change of the area A, of the circle with respect to its circumference C i.e dA/dC.

Answer 1

a) Increase:

$$(-\infty,-5)\ and\ (3,\infty)$$

Decrease:

$$(-5,3)$$

b) Downwards:

$$(-\infty,-1)$$

Upwards:

$$(-1,\infty)$$