1. ## derivatives

what is the first and second derivative of:

f(x) = (x^(2/3))(x-5)

2. Hello,

$(x^{2/3})(x-5)=x^{5/3}-5x^{2/3}$

The derivative for $x^a$ is $ax^{a-1}$

This is all you need...

3. ## i need a little more help

for the first derivative i got f'(x) = (5/3)(x^(2/3)) - (10/3)(x^(-1/3))...... but i need to be able to get the critical numbers for this and i can't figure out what they are. I know i am suppose to set the equation equal to 0 but i still can't get it. And i have to show my work so I'm not suppose to use a calculator.

4. The first derivative is correct

Solve for x in :
$f'(x) = (5/3)(x^{2/3}) - (10/3)(x^{-1/3})=0$

$\frac{5}{3} x^{2/3}-\frac{10}{3} \frac{1}{x^{1/3}}=0$

Assuming that x is different from 0 (from the beginning ^^)

Multiply both sides by x^(1/3)

$\frac{5}{3} x^{2/3+1/3}-\frac{10}{3}=0$

$\frac{5}{3} x - \frac{10}{3}=0$

Do you see the critical point ? ^^

5. yes thank you...

Now i'm having trouble with the 2nd derivative... if i have f'(x) = (5/3)(x^(2/3)) - (10/3)(x^(-1/3))... then does the 2nd derivative f"(x) = (10/9)(x^(-1/3)) + (10/9)(x^(-4/3)) ???