Question

Find the curvature of the function f(x) = 3x^3 + 4680x^2 + 1789x + 181 at x = -520.

(a) 1

(b) 0

(c) ∞

(d) -520

I had been asked this question at a job interview.

The question is from Curvature topic in chapter Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (b) 0

To explain I would say: For a Cubic polynomial the curvature at  x = ^-b⁄3a is zero because f^”(x) is zero at that point.

Looking at the form of the given point we can see that  x = ^-4680⁄3*3 = -520

Thus, curvature is zero.