Question

Let f(x) be positive, continuous and differentiable on the interval (a, b) and $\lim _ { \mathrm { x } \rightarrow \mathrm { a } ^ { + } }$ f(x) = 1, $\lim _ { \mathrm { x } \rightarrow \mathrm { b } ^ { - } }$ f(x) = 3^1/4.

If f ¢(x) ³ f ³(x) + then the greatest value of b – a is -

• A. 1
• B. 3^1/4
• C. (3^1/4 – 1)
• D. $\frac { \pi } { 4 }$f

Answer 1

Answer: (D)

$\frac { \pi } { 4 }$f

Answer 2

f ¢ (x) ³ f ³ (x) + Ž ³ 1

Integrating on the interval (a, b), we get

dx ³

Ž $\frac { 1 } { 2 }$ tan^–1 ³ b – a

Ž b – a £ $\frac { 1 } { 2 }$ = $\frac { \pi } { 24 }$