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Find the range of function, f: [0,1] -> ...

Find the range of function, f: [0,1] -> R, `f(x)= x^3-x^2+4x+2sin^-1x .`

A

`[-pi -2, 0]`

B

`[2,3]`

C

`[0,4+pi]`

D

`(0,2+pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
`because f(x)=x^3-x^2+4x+2 sin^(-1) x`
`therefore f'(x)=3x^2 -2x+4 + 2/sqrt(1-x^2) > 0 AA x in [0,1)`
`therefore` f(x) is increasing function
Range = `[f(0),f(1)] rArr [0,4+pi]`
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