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Let f(x)=cospix+10x+3x^2+x^3, x in [-2...

Let
`f(x)=cospix+10x+3x^2+x^3, x in [-2,3]`
The absolute miniumum value of f(x) is

A

0

B

-15

C

`3-2pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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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OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Chapter Test
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  3. If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 ...

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  4. The greatest value of the funxtion f(x)=xe^(-x) " in " [0,oo] is

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  5. Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

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  6. In the right triangle BAC, angle A=pi/2 and a+b=8. The area of the tr...

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  7. The range of values of a for which the function f(x)=(a^2-7a+12)cosx...

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  8. If the function f(x) = (2a-3)(x+2 sin3)+(a-1)(sin^4x+cos^4x)+log 2...

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  9. The function f(x)=(ax+b)/((x-1)(x-4)) has a local maxima at (2,-1), th...

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  10. For x > 1, the minimum value of 2 log10(x)-logx(0.01) is

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  11. The maximum valu of the function f(x) given by f(x)=x(x-1)^2,0ltxlt2...

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  12. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

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  13. The minimum value of f(x)=e^((x^4-x^3+x^2)) is

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  14. If the function f(x)=a/x+x^2 has a maximum at x=-3 then a=

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  15. Find the maximum value of 4sin^2x+3cos^2+sinx/2+cosx/2dot

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  16. The least value of the f(x) given by f(x)=tan^(-1)x-1/2 logex " in t...

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  17. The slope of the tangent to the curve y=e^x cosx is minimum at x= a,0 ...

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  18. The value of a for which the function f(x)={{:(tan^(-1)a -3x^2" , " ...

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  19. The minimum value of 27^(cos3x)81^(sin3x) is

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  20. If f(x)=(x^2-1)/(x^2+1) , for every real x , then the maximum value o...

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  21. f(x) = |x|+|x-1| +|x-2|, then which one of the following is not correc...

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