Please show all steps gz 3 22r 1 Solutiongx 3 2x 173 Diffe

Please show all steps.

Solution

g(x) = 3 (2x - 1)^7/3

Differentiate wrt x

g\'(x) = 3 * (7/3) (2x - 1)^4/3*2

g\'(x) = 14 (2x - 1)^4/3

Equate to 0 we get

0 = 14 (2x - 1)^4/3

x = 1/2

Interval = (-infinity , 1/2) and (1/2 , infinity)

Take a value from every interval and find the sign they have in the first derivative.

If g\'(x) > 0 is increasing.

If g\'(x) < 0 is decreasing.

Take x = 0 ; g(x) = - 14 Hence , g(x) < 0 So it is decreasing in the interval (-infinity , 1/2)

Take x = 1 ; g(x) = 14 Hence , g(x) > 0 So it is increasing in the interval (1/2 , infinity)