isi-entrance 2014 Q13

isi-entrance · India · solved Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

Let $f(x) = ax^3 + bx^2 + cx + d$ be a strictly increasing function with $a > 0$. Define $g(x) = f'(x) - 6ax - 2b + 6a$. Then $g(x)$ is
(A) always negative (B) always positive (C) sometimes positive sometimes negative (D) always zero

(B) $g(x)$ is always positive.

Let $f(x) = ax^3 + bx^2 + cx + d$ be a strictly increasing function with $a > 0$. Define $g(x) = f'(x) - 6ax - 2b + 6a$. Then $g(x)$ is

(A) always negative \quad (B) always positive \quad (C) sometimes positive sometimes negative \quad (D) always zero

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q17 Q18 Q20 Q21 Q22 Q24 Q25