Question

The curvature of a function  depends directly on leading coefficient when x=0 which of the following could be   f(x)?

(a) y = 323x^3 + 4334x + 10102

(b) y = x^5 + 232x^4 + 232x^2 + 12344

(c) y = ax^5 + c

(d) y = 33x^2 + 112345x + 8945

The question was asked in final exam.

The doubt is from Curvature in section Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (d) y = 33x^2 + 112345x + 8945

The explanation is: Using formula for curvature

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

Observe numerator which is f”(x)

Now this second derivative must be non zero for the above condition asked in the question

Looking at all the options we see that only quadratic polynomials can satisfy this.