Expert: Ahmed Salami - 1/19/2009

Question
Hello,
I'm having a problem finding the horizontal tangent line of this eqt.  
f(x)= x^5/3-5x^2/3+1
i kno im supposed to find the derivative first...but i keep getting the wrong answer so i'd appreciate it if u can show me how to do it in steps.

Please and Thank you!!

Answer
Hi Mariam,
Well, the horizontal tangent line occurs when the derivative is zero.
f(x) = x^5/3 - 5x^2/3 + 1
f'(x) = 5x^4/3 - 10x/3
equating this to zero, we get
5x^4/3 - 10x/3 = 0
multiply through by 3
5x^4 - 10x = 0
divide through by 5
x^4 - 2x = 0
x(x^3 - 2) = 0
either x = 0 or x^3 - 2 = 0
x = 0 or x^3 = 2
x = 0 or x = cube root 2

Regards