# Find all the values of x (if any) where the tangent line to the graph of the....

• Sep 3rd 2008, 09:53 PM
plstevens
Find all the values of x (if any) where the tangent line to the graph of the....
....function is horizontal.
x cubed - 12x + 2

wouldn't that be 0 and 2. by taking the derivative and solving for x, i get only 2, how do i find the other number(s)?
• Sep 3rd 2008, 09:56 PM
Chris L T521
Quote:

Originally Posted by plstevens
....function is horizontal.
x cubed - 12x + 2

wouldn't that be 0 and 2. by taking the derivative and solving for x, i get only 2, how do i find the other number(s)?

The derivative is $\displaystyle 3x^2-12$

Setting it equal to zero, we get $\displaystyle x^2-4=0\implies x^2=4\implies x={\color{red}\pm}2$

These are the only values where the function has horizontal tangents.

Does this make sense?

--Chris
• Sep 3rd 2008, 10:02 PM
11rdc11
Hi to find a horizontal tangent line to a function you take the derivative and equal it to 0

$\displaystyle f(x) = x^3 -12x+2$

$\displaystyle f'(x) = 3x^2 -12$

$\displaystyle 0= 3x^2 -12$

$\displaystyle x = 2$ and $\displaystyle x = -2$

Shoot to late again lol
• Sep 3rd 2008, 10:03 PM
plstevens
thanks
• Sep 3rd 2008, 10:14 PM
plstevens
Find the derivative
9x^7/5-5x^2+10^4

Now here i worked this out but the computer keep saying my answer of 63/5x^2/5-10x
• Sep 3rd 2008, 10:14 PM
plstevens
the computer keep saying its wrong, where did i possibly go wrong on this one
• Sep 3rd 2008, 10:46 PM
11rdc11
$\displaystyle 9x^{\frac{7}{5}} - 5x^2+10^4$

Is this what it looks like?