# Thread: The critical numbers of the function

1. ## The critical numbers of the function

f(t)=6^(2/3)+t^(5/3)

I understand I take the derivative of the function and set it equal to zero to find the critical numbers, however I get stuck after I take the derivative

f'(t)=4t^(-1/3)+5/3t^(2)=0

2. Originally Posted by Asuhuman18
f(t)=6^(2/3)+t^(5/3)

I understand I take the derivative of the function and set it equal to zero to find the critical numbers, however I get stuck after I take the derivative

f'(t)=4t^(-1/3)+5/3t^(2)=0
I guess you meant f(t) to be ...

$f(t) = 6t^{2/3} + t^{5/3}$

$f'(t) = 4t^{-1/3} + \frac{5}{3}t^{2/3} = t^{-1/3}\left(4 + \frac{5}{3}t \right) = 0$

can you finish?

3. Originally Posted by skeeter
I guess you meant f(t) to be ...

$f(t) = 6t^{2/3} + t^{5/3}$

$f'(t) = 4t^{-1/3} + \frac{5}{3}t^{2/3} = t^{-1/3}\left(4 + \frac{5}{3}t \right) = 0$

can you finish?
yeah sorry about that...Thanks for all the help