Question

Consider the following. (If an answer does not exist, enter DNE.) f(x) = 2x³ - 9x²+ 9x - 4. Find the interval(s) on which f is concave up. (Enter your answer using interval notation.)

Answer 1

The interval(s) on which the function f(x) = 2x³ - 9x² + 9x - 4 is concave up is (1.5, ∞).

Step-by-step explanation:

To find the interval(s) on which the function f(x) = 2x³ - 9x² + 9x - 4 is concave up, we need to find where the second derivative of the function is positive. To do this, we need to find the second derivative of f(x) and solve it for x:

f''(x) = 12x - 18

Setting f''(x) > 0, we get:

12x - 18 > 0

12x > 18

x > 1.5

The interval on which f(x) is concave up is (1.5, ∞).