Question

Please help, I am so confused.
Determine if the graphs of each of the following functions is increasing or decreasing, concave up or concave down.

(a) y = 1.6(6)−x.
increasing
decreasing

concave up
concave down


(b) y = 40 − 40e−0.7x.
increasing
decreasing

concave up
concave down

Answer 1

If \(\large \frac{dy}{dx}\) > 0 in an interval, the function is increasing in that interval.
If \(\large \frac{dy}{dx}\) < 0 in an interval, the function is decreasing in that interval.

Answer 2

If \(\large \frac{d^2y}{dx^2} > 0\) in an interval, the function is concave up in that interval.
If \(\large \frac{d^2y}{dx^2} < 0\) in an interval, the function is concave down in that interval.

Answer 3

You can also answer this question without using calculus if you know the general shapes of standard graphs. Or you can plot them using a graphing calculator 9also available online) and see where it is increasing / decreasing and concave up / down.