Question

Help with differentiating
f(x) = x^a - x^2a
a is a positive integer
I need to find out for what values of X the slope increases and decreases

Answer 1

As in where the function f(x) is increasing and decreasing.

Answer 2

you can call it f(x) = y = x^a - x^2a

Answer 3

I find myself stuck around here after differentiating:
\[a(x ^{a-1)}-2x ^{2(a-1)})\]

Answer 4

\[a(x^{a-1}-2x^{2a-1})\]

Answer 5

Yes of course, but I dont understand how to proceed to find out where the slope of the function is increasing/decreasing (and possibly a maximum and minimum)

Answer 6

You can find the roots of it, then use values less than and more than the actual value to figure out whether it gives positive or negative result

Answer 7

Here are the roots,
\[\large x=( \frac{1}{2})^{\frac{1}{a}}\]
\[\large x=0\]
Use values larger or less than the roots to figure out whether its increasing or decreasing.