Question

if a function is concave down and increasing, what can we say about its slope?
a. the slope is negative and decreasing
b. the slope is positive but decreasing
c. the slope is constant
d. the slope is positive and increasing

Explanation:

Step1: Recall function properties

A function is increasing when its first - derivative (slope) is positive.

Step2: Recall concavity property

A function is concave down when its second - derivative is negative. A negative second - derivative means the first - derivative (slope) is decreasing.

Answer:

B. The slope is positive but decreasing