Question

Find all critical numbers for the function
f(x) = x^(1/6) - x^(-5/6)

Answer 1

i know you need the derivative and then put it equal to 0 but I'm not sure what to do about the fractional exponents.

Answer 2

apply power rule to each term, don't be afraid of these exponents.

Answer 3

\[(1/6)x^{-5/6}-(-5/6)x^{-11/6}=0\]

Answer 4

well, the derivative of y, or the f(x) is written either as y' (y prime, or as dy/dx)

Answer 5

\[f'(x)=\frac{1}{6}x^{-5/6}+\frac{5}{6}x^{-11/6}\]

Answer 6

f prime x.

Answer 7

btw, are you given any interval, on which you are finding critical numbers?

Answer 8

The boundaries of a closed interval would be also critical numbers.

Answer 9

I think if i multiply both sides by x^5/6 it simplies the problem. nevermind i got it from here. thanks for the help