Find the x-coordinates of any relative extrema and inflection point(s) for the function f of x equals 9 times x raised to the one third power plus 9 halves times x raised to the four thirds power . you must justify your answer using an analysis of f ? (x) and f ).

reletive extrema are where the first derivitive is 0 and the sign of the first derivitive changes

inflection points are where the 2nd derivitive is 0 and the sign of the 2nd derivitive changesd

I use f'(x)=1st derivitive and f''(x)=2nd derivitive

remember power rule:

f'(x)

f''(x)

I'm not going to show the work for solving for when f'(x)=0 and f''(x)=0 because at this stage of the game, you should be able to do that easily

f'(x) is equal to 0 when x=-0.5, the sign changes from negative to positive at this point so at this point, the function has a relative minimum

f''(x) is equal to 0 when x=1, the sign changes from negative to positive at this point so at this point, the function is changing from concave down to concave up

step-by-step explanation: