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Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,...

Let `f(x)={(|x-2|+a^2-9a-9`,ifx`lt`2, `2x-3 `,ifx`ge`2:} Then find value of 'a' for which f(x) has local minima at x= 2

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. In a right -angled triangle, prove that r+2R=S.

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  2. Show that the semivertical angle of a cone of maximum volume and of gi...

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  3. Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,ifxge2:} Then find value of 'a...

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  4. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

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  5. The difference between the greatest and least values of the function f...

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  6. The tangent and normal to the curve y=2sinx+sin2x are drown at P(x=pi/...

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  7. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

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  8. Find the point on the curve y-e^(xy)+x=0. At which we have vertical ta...

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  9. Find the lengths of tangent, subtangent, normal and subnormal to y^2=4...

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  10. If the length of subnormal is equal to length of subtangent at a point...

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  11. Find the angle of intersection between the following curves, y^2=4x an...

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  12. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

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  13. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

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  14. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

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  15. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  16. Verify Rolle's theorem for f(x)=x^3(x-1)^2 in the interval 0lexle1

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  17. If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

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  18. The value of 'c' of Rolls's throrem is applicable to the function f(x)...

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  19. Find 'c' of the Lagrange's mean value theorem for the function f(x)=3x...

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  20. If A(x1,y1) an B(x2,y2) be two points on the curve y=ax^2+bx+c then La...

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