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How many roots of the equation (x-1)(x-2...

How many roots of the equation `(x-1)(x-2)(x-3)+(x-1)(x-2)(x-4) +(x-2)(x-3)(x-4)
+(x-1)(x-3)(x-4)=0` are positive?

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CENGAGE-APPLICATION OF DERIVATIVES-Examples
  1. Discuss the applicability of Rolles theorem for the following functi...

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  2. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

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  3. How many roots of the equation (x-1)(x-2)(x-3)+(x-1)(x-2)(x-4) +(x-2)(...

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  4. If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has at...

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  5. Let f(x) be differentiable function and g(x) be twice differentiable f...

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  6. Let f(x) be differentiable function and g(x) be twice differentiable f...

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  7. If f : [-5, 5] to R is a differentiable function function and if f'(x)...

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  8. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

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  9. Let f:[2,7]vec[0,oo) be a continuous and differentiable function. Then...

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  10. Let f(x)a n dg(x) be differentiable function in (a , b), continuous at...

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  11. Using Lagranges mean value theorem, prove that |cosa-cosb|<|a-b|dot

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  12. Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)...

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  13. Suppose alpha,betaa n dtheta are angles satisfying 0<alpha<theta<bet...

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  14. Let f be continuous on [a , b],a >0,a n d differentiable on (a , b)dot...

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  15. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

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  16. If the area of the triangle included between the axes and any tangent ...

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  17. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

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  18. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

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  19. Find the condition for the line y=m x to cut at right angles the conic...

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  20. If the curves ax^(2) + by^(2) =1 and a(1) x^(2) + b(1) y^(2) = 1 inte...

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