Question

If at each point of the curve y = x³ –ax² + x + 1, the tangent is inclined at an acute angle with the positive direction of x- axis, then

• A. a > 0
• B. a £$\sqrt{3}$
• C. –$\sqrt{3}$£ a £$\sqrt{3}$
• D. None

Answer 1

Answer: (C)

–$\sqrt{3}$£ a £$\sqrt{3}$

Answer 2

$\frac{dy}{dx}$ = 3x² – 2ax + 1 ³ 0;

Q A = 3 > 0 Ž D £ 0 Ž 4a² – 12 £ 0

Ž –$\sqrt{3} \leq a \leq \sqrt{3}$