Question

Let f(x)=4x−−√−4x for x>0. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

Answer 1

Step-by-step explanation:

f(x) = ∫πy²dx = ∫π(4x - √-4x)² = ∫π(16x² - 8x√-4x + 4x)dx

Divide through by 4x: f(x) = ∫π(4x -2√-4x + 1)dx limit (0,1)

= π{2x² + 1/4(-4x)^1/2 + x) limit (0,1)

= π( 2 + 1/8 + 1) = π(25/8) = 3.125π