Question

Find the curvature k of the curve given by f(x) = 2x²?

Answer 1

The curvature of the curve given by f(x) = 2x² is 4.

Step-by-step explanation:

The curvature of a curve given by the function f(x) = 2x² can be found by taking the second derivative of the function and then evaluating it at a specific value of x.

To find the second derivative, we first take the first derivative of the function f(x):

f'(x) = 4x

Then, we take the derivative of f'(x) to find the second derivative:

f''(x) = 4

The curvature, k, is equal to the absolute value of the second derivative:

k = |f''(x)| = 4