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Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 -...

Let f(x) = Max. `{x^2, (1 - x)^2, 2x(1 - x)}` where `x in [0, 1]` If Rolle's theorem is applicable for f(x) on largest possible interval [a, b] then the value of `2(a+b+c)` when `c in [a, b]` such that f'(c) = 0, is

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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Passage Based Questions)
  1. Let f(x)=(1)/(1+x^(2)), let m be the slope, a be the x-intercept and ...

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  2. Evaluate (5!)/(1! 3!) × (7!)/(6! 3!)

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  3. Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 - x)} where x in [0, 1] If Rol...

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  4. Evaluate (3!)/(2! 2!) × (8!)/(7! 4!)

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  5. Find the value of (2! + 3! - 1!)

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  6. Find the value of (10!)/(6! × 3! × 5!)

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  7. Solve : 1/(x + 1) + 4/(3x + 6) = 2/3

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  8. In the non-decreasing sequence of odd integers (a(1),a(2),a(3),....)={...

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  9. In the non-decreasing sequence of odd integers (a(1),a(2),a(3),....)={...

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  10. In the non-decreasing sequence of odd integers (a(1),a(2),a(3),....)={...

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  11. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

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  12. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

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  13. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

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  14. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

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  15. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

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  16. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

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  17. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

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  18. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

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  19. consider the function f(x)=(x^(2))/(x^(2)-1) The interval in which f...

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  20. consider the function f(x)=(x^(2))/(x^(2)-1) If f is defined from R-...

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