Question

The curvature of a function f(x) is zero. Which of the following functions could be f(x)?

(a) ax + b

(b) ax^2 + bx + c

(c) sin(x)

(d) cos(x)

This question was posed to me by my college professor while I was bunking the class.

This key question is from Curvature in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) ax + b

The best explanation: The expression for curvature is

k=\(\left |\frac{f”(x)}{(1+[f'(X)]^2)^{\frac{3}{2}}} \right |\)

Given that k = 0 we have

f^” (x) = 0

f(x) = a + b.