Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable

Question

f(x)= 4x/(x²+1)

what is the

relative maximum=

relative minimum=

Answer 1

f'(x) = 4(x² + 1 - 2x²)/(x² + 1)² = 4(1 - x²)/(x² + 1)² = 0; x² - 1 = 0; x = ±1 are critical numbers.

f''(x) = 4[- 2x(x² + 1) - 4x(1 - x²)]/(x² + 1)³ = 4(2x³ - 6x)/(1 + x²)³;

f''(1) = - 2 < 0 so at x = 1 is local maximum (1, 2)

f''(- 1) = 2 > 0 so at x = - 1 is local minimum (- 1, - 2)