Question

Consider the following: g(x) = 9x^(4/5) - 4x^(9/5)

(a) Find the interval(s) of increase. (Enter your answer using interval notation.)

a) (-[infinity], 0)
b) (0, [infinity])
c) (0, 1)
d) (1, [infinity])

Answer 1

The interval of increase for the function g(x) = 9x^(4/5) - 4x^(9/5) is (0, 1).

Step-by-step explanation:

To find the intervals of increase for the function g(x) = 9x^(4/5) - 4x^(9/5), we need to determine where the derivative of the function is positive.

To do this, we find the derivative of g(x) and set it greater than zero.

The derivative of g(x) is g'(x) = (36/5)x^(-1/5) - (36/5)x^(4/5).

Setting g'(x) > 0, we can solve for x to find the interval(s) of increase for g(x).

The interval of increase is (0, 1) [Option c)].