Question

For the function f(x) = - 2x³ + 54x + 15,

Find all intervals where the function is increasing. Answer: f i

Answer 1

To find the intervals where the function is increasing, set the derivative f'(x) equal to zero and solve for x. The function is increasing for x < 3 and decreasing for x > 3.

Step-by-step explanation:

To find the intervals where the function is increasing, we need to find the values of x where the derivative of f(x) is positive. The derivative of f(x) is f'(x) = -6x²+54. Setting this derivative equal to zero and solving for x, we find x = 3. This means that the derivative changes sign at x = 3, so the function is increasing for x < 3 and decreasing for x > 3.