Consider the following function.

f(x) = (4 − x)e−x

(a) find the intervals of increase or decrease. (enter your answers using interval notation.)

increasing
decreasing (b) find the intervals of concavity. (enter your answers using interval notation. if an answer does not exist, enter dne.)concave up concave down

The table shows the balance of a money market account over time. write a function that represents the balance y (in dollars) after t years.

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. answer to the nearest integer.