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Let the tangent to the graph of y=f(x) a...

Let the tangent to the graph of `y=f(x)` at the point `x = a` be parallel to the x-axis and let `f'(a-h) > 0 and f(a+h) <0,` where `h` is a very small positive number.Then, the ordinate of the points is

A

a maximum

B

a maximum

C

both a maximum and a mimum

D

neither a maximum nor a minimum

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`f(a - it ) gt 0`
`rArr` f(x) is increasing in the left neighbourhood of =a
`f(a+h) lt 0`
`rArr` f(x) is decreasing in the right neigh bourhood of x=a
`therefore` f(a) is a local maximum value of f(x)
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OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Chapter Test
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  2. The maximum value of (1/x)^(2x^2) IS =

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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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