Final answer:
To find the curvature κ of a plane curve y = 2x^2 + 3x - 3 at x = 1, we can first find the second derivative of the equation, which is 4. Therefore, the curvature κ of the curve at x = 1 is 4.
Step-by-step explanation:
To find the curvature κ of a plane curve, we need to find the second derivative of the equation and then evaluate it at the given point. The equation of the curve is y = 2x^2 + 3x - 3.
Taking the first derivative, we get dy/dx = 4x + 3. Taking the second derivative, we get d^2y/dx^2 = 4.
To find the curvature at x = 1, substitute x = 1 into the second derivative: d^2y/dx^2 = 4.
Therefore, the curvature κ of the curve at x = 1 is 4.