Question

Suppose that f(x)=2x³ −3x² −36x+4

a. On which intervals is f(x) increasing? (Use I for infinity and - I for negative infinity.) Enter the intervals in increasing order. 3 and they are both negative when x<1. Conclusion: Factor the derivative. It is something like this, but different. b. Where is f(x) concave up?

Answer 1

To ascertain where the function f(x) is increasing and concave up, the first and second derivatives, f'(x) and f''(x), need to be calculated and analyzed for positivity.

Step-by-step explanation:

The question involves determining the intervals on which the function f(x)=2x³ −3x² −36x+4 is increasing and where the function is concave up. To find where f(x) is increasing, we calculate the first derivative, f'(x), and find the intervals where f'(x)>0. For concavity, we look at the second derivative f''(x) and determine where it is positive (concave up).

To find the increasing intervals, we must solve f'(x)>0, which typically involves finding the critical points by setting f'(x)=0 and using a sign chart to assess where the derivative is positive. Concavity is determined by solving f''(x)>0.

The specific intervals for increasing behavior and concavity cannot be determined from the given information without further computation.