# Thread: How to find the critical point of this?

1. ## How to find the critical point of this?

f(x)=x^(10)e^(−13x)

The derivative is f(x)=(10x^(9)−13x^(10)) * e^ (−13x)
The derivative is right because its given, I don't understand how solve for x = 0 correctly to find the critical points.. can someone direct me?
I would have thought x = 0 and sqrt(10/13) but apparently i not correct.

2. The derivative factorises further to $\displaystyle f'(x) = x^9(10 - 13x)e^{-13x}$.

Set this equal to $\displaystyle 0$ and solve for $\displaystyle x$ using the null factor law.

3. Originally Posted by ASUSpro
f(x)=x^(10)e^(−13x)

The derivative is f(x)=(10x^(9)−13x^(10)) * e^ (−13x)
The derivative is right because its given, I don't understand how solve for x = 0 correctly to find the critical points.. can someone direct me?
I would have thought x = 0 and sqrt(10/13) but apparently i not correct.
No, the derivative is f'(x)=(10x^(9)−13x^(10)) * e^ (−13x).

You're expected to solve f'(x) = 0, that is, 10x^(9)−13x^(10) = 0.