Question

f(x) = 2sin³x – 3sin²x + 12sinx + 5 ∀ x ∈ $\left( 0 , \frac { \pi } { 2 } \right)$ then

• A. 'f ' is increasing in$\left( 0 , \frac { \pi } { 2 } \right)$
• B. 'f is decreasing in$\left( 0 , \frac { \pi } { 2 } \right)$
• C. 'f is increasing in$\left( 0 , \frac { \pi } { 4 } \right)$and decreasing $\left( \frac{\pi}{4},\frac{\pi}{2} \right)$
• D. 'f ' is decreasing in $\left( 0,\frac{\pi}{4} \right)$ and increasing in $\left( \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$

Answer 1

Answer: (A)

'f ' is increasing in$\left( 0 , \frac { \pi } { 2 } \right)$

Answer 2

f '(x) = 6 cosx (sin²x − sinx + 2) > 0 ∀

x ∈ (0, π/2) thus f(x) is increasing in (0, π/2).