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Prove that for any two numbers x1a n dx2...

Prove that for any two numbers `x_1a n dx_2dot` `(e^(2x_1)+e^(x_2))/3> e^((2x_1+x_2)/3)`

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MOTION-MAXIMA AND MINIMA -EXERCISE - 4 (LEVEL - II)
  1. Prove that for any two numbers x1a n dx2dot (e^(2x1)+e^(x2))/3> e^((2...

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  2. The total number of local maxima and local minima of the function f(x)...

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  3. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  4. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  5. Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (...

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  6. Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and u...

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  7. The maximum value of the function f(x)=2x^(3)-15x^(2)+36x-48 on the se...

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  8. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  9. Let f be a function defined on R (the set of all real numbers) such th...

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  10. The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0

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  11. Let p(x) be a real polynomial of least degree which has a local maximu...

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  12. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

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  13. If f(x) = underset(0)overset(x)inte^(t^(2)) (t-2) (t-3) dt for all x ...

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  14. A rectangular sheet of fixed perimeter with sides having their lengths...

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  15. The function f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a lo...

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  16. Let f:RtoR and g:RtoR be respectively given by f(x)=|x|+1 and g(x)=x^(...

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  17. A cylindrical container is to be made from certain solid material with...

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  18. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

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