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If ma and M respectively denote the mini...

If ma and M respectively denote the minimum and maximum of `f(x) =(x-1)^2+3` for `x in [-3,1]` then the ordered pair (m,M)=

A

(-3,19)

B

(3,19)

C

(-19 , 3)

D

(-19 ,-3)

Text Solution

Verified by Experts

The correct Answer is:
B
We have `f(x)=x(x-1)^2+3`
`rArr f(x)=2 (x-1) lt 0 " for all " x in [ -3,1]`
So f(x) is decreasing [-3 , 1]
`rArr m=f(1)` and M = f (-3) `rArr` m=3 and M=19 (m,M)=(3,19 )
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OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Chapter Test
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  11. The maximum value of the function f(x) given by f(x)=x(x-1)^2,0ltxlt...

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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. Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value o...

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  15. Find the maximum value of 4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2...

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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 number x , then the minimum v...

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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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