Final answer:
The x-coordinate of the point of maximum curvature on the curve y = 2e⁵x is 0, and the maximum curvature is -50.
Step-by-step explanation:
To find the x-coordinate of the point of maximum curvature on the curve y = 2e⁵x, we need to find the second derivative of the function and set it equal to zero. The second derivative can be found by taking the derivative of the first derivative. The first derivative of y = 2e⁵x is y' = 10e⁵x. Taking the derivative again, we get y'' = 50e⁵x.
Setting y'' equal to zero, we have 50e⁵x = 0. Solving for x, we find that x = 0. Since the curvature is negative at x = 0, the maximum curvature is -50.