ABSOLUTE Maximum and Minimum

Question

Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = x/(81+x^2)

Answer 1

f'(x) = (81 + x² - 2x²)/(81 + x²)² = (81 - x²)/(81 + x²)² = 0; 81 - x² = 0; x² = 81; x = ± 9

f(9) = 9/(81 + 81) = 1/18 abs max

f(-9) = -9/(81 + 81) = - 1/18 abs min

By second derivative test

Answer 2

This function is defined on the whole real line and goes to zero as |x|->∞.

Use the quotient rule to find the derivative and set it equal to 0.

Solve for x.

You can check the 2nd derivative text to see which values are at max and min...or you can graph it.