Question

Let L1 denote the line y = 3x + 2 and L2 denote the line y = 4x + 3. Suppose that f: ℝ → ℝ is a four times continuously differentiable function such that the line L1 intersects the curve y = f(x) at exactly three distinct points and the line L2 intersects the curve y = f(x) at exactly four distinct points. Then, which one of the following is TRUE ?

• A. $\frac{df}{dx}$ does not attain the value 3 on $\R$
• B. $\frac{d^2f}{dx^2}$ vanishes at most once on $\R$
• C. $\frac{d^3f}{dx^3}$ vanishes at least once on $\R$
• D. $\frac{df}{dx}$ does not attain the value $\frac{7}{2}$ on $\R$

Answer 1

Answer: (C)

$\frac{d^3f}{dx^3}$ vanishes at least once on $\R$

Answer 2

The correct option is (C) : $\frac{d^3f}{dx^3}$ vanishes at least once on $\R$.