Question

y = x
(a) Find the intervals on which is
increasing
(b) Find the intervals on which is
decreasing
(c) Find the open intervals on which is
concave up.
(d) Find the open intervals on which is
concave down
​

Answer 1

Step-by-step explanation:

On the first interval, the second derivative is negative, which means the function is concave down. On the second interval, the second derivative is positive, which means the function is concave up. (Plug in values on the intervals into the second derivative and see if they are positive or negative.

In determining intervals where a function is concave upward or concave downward, you firstfind domain values where f″(x) = 0 or f″(x) does not exist. Then test all intervals around these values in the second derivative of the function. If f″(x) changes sign, then ( x, f(x)) is a point of inflection of the function.