Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3....

Let `f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3.` The absolute minimum value of `f(x)` is 0 (b) `-15` (c) `3-2pi` none of these

-15

`3-2pi`

none of these

Text Solution

Verified by Experts

The correct Answer is:

We have
`f(x)=cospi x+10x+3x^2+x^3`
`rArr f'(x)=-pisin pi x+10+x+3x^2`
`rArr f'(x)=3 (x+1)^2+ (7-pi sin pi x)gt for all x in [-2,3]`
`rArr f(x) " is stricly increasing on " [-2,3]`
`therefore` Absolute minimum value of f(x)
`=f(-2)=cos2 pi-20+12-8=-15`

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