Question

If the derivative of the function $\lim_{n \rightarrow \infty}$is everywhere continuous and differentiable at x = 1 then

• A. a = 2, b = 3
• B. a = 3, b = 2
• C. a = –2, b = – 3
• D. a = – 3, b = – 2

Answer 1

Answer: (A)

a = 2, b = 3

Answer 2

To find a, b we must have two equations in a, b

Since $f ( x )$ is differentiable, it must be continuous at $x = - 1$.

$\therefore$ $R = L = V$ at $x = - 1$ for f(x) $\Rightarrow b - a + 4 = a + b$

$\therefore 2 a = 4 \quad$ i.e., $a = 2$

Again $f ^ { \prime } ( x )$ is continuous, it must be continuous at $x = - 1$.

$\therefore R = L = V$ at $x = - 1$ for $f ^ { \prime } ( x )$

$- 2 b + a = - 2 a$ Putting $a = 2$ we get $- 2 b + 2 = - 4$

$\therefore 2 b = 6$ or $b = 3$