Final answer:
To find the curvature of the function y=4x^4, calculate the second derivative of y with respect to x and substitute the value of x into the second derivative.
Step-by-step explanation:
The curvature of a function can be found using the formula: y=4x^4. To find the curvature, we need to calculate the second derivative of y with respect to x.
- First, find the first derivative of y using the power rule which states that the derivative of x^n is nx^(n-1). In this case, the first derivative of y = 4x^4 is dy/dx = 16x^3.
- Next, find the second derivative of y by differentiating the first derivative. The second derivative of y = 16x^3 is d^2y/dx^2 = 48x^2.
- Now, substitute the value of x into the second derivative to find the curvature. For example, if x = 2, the curvature is 48 * (2^2) = 48 * 4 = 192.