# Thread: point of max curvature of f(x) = 8e^3x

1. ## point of max curvature of f(x) = 8e^3x

f(x) = 8e^3x
f'(x) = 24e^3x
f''(x) = 72e^3x

k(x) = f''(x) / (1 + [f'(x)]^2) ^ (3/2)

k(x) = 72e^3x / (1 + 576e^6x) ^(3/2)

now I know i need to find k'(x) and set it equal to 0 and solve for x, but I just cant seem to come up with an appropriate answer. =/

k'(x) = long complicated quotient rule expression whose value of x escapes me.

please help!

thanks!

2. Here's a little trick you can use, if you like: write the denominator in the numerator with opposite sign of the exponent, and use product rule instead. It'll get you the same result, but sometimes it's easier.

3. Another useful point: a fraction is equal to 0 if and only if its numerator is 0. You can just ignore the denominator.