Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Question

y = x

36 − x2

increasing =

decreasing =

 

 

Answer 1

x √(36-x²) is defined on [-6, 6] equals 0 at -6, 0, and 6, and will have a minimum on (-6, 0) and a maximum on (0, 6)

f'(x) = √(36-x²) - x²/(36-x²) = (36 - 2x²)/√(36-x²)

(36 - 2x²) = 0 at ±3√2

The function decreases on (-6, -3√2) and (3√2, 6) and increases on (-3√2, 3√2)