Question

Let

­ƒ(x) = then

number of points (where ƒ(x) attains its minimum value) is –

• A. 1
• B. 2c
• C. 3
• D. ) Infinite many

Answer 1

Answer: (A)

1

Answer 2

ƒ(x) =

Let g(x) = x³ + x² + 3x + sin x

\ g¢ (x) = 3x² + 2x + 3 + cos x

= 3 + cos x

= 3 $\left\{ \left( x + \frac { 1 } { 3 } \right) ^ { 2 } + \frac { 8 } { 9 } \right\}$ + cos x > 0

and 2 < 3 + sin < 4

Hence minimum value of ƒ(x) is 0 at x = 0

Hence number of points = 1.