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If tangent at point P(a,b) to the curve `x^3+y^3=c^3` meet the curve agins at `Q(a_1, b_1)` then `(a_1)/a +b_1/b=`

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Let f(x) be an decreasing function defined on (0,oo). If f(3a^2-4a+1)g...

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  2. The curve y=ax^3+bx^2+cx+d cut y axis at (0.5) where gradient is 3 cur...

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  3. If tangent at point P(a,b) to the curve x^3+y^3=c^3 meet the curve agi...

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  4. Find the number of solutions of the equation x^3+2x^2+5x+2cosx=0 in [0...

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  5. The maximum area of a rectangle that can be inscribed in a circle of r...

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  6. If x+4y=14 is a normal to the curve y^2=ax^3 -betaat (2,3) then value ...

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  7. If f(x) and g(x) are differentiable function for0lexle1such that f(0)=...

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  8. If ax^2+b/xgecfor all positive x where agt0andbgtc show that 27ab^2ge4...

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  9. find all the tangents to the curve y=cos(x+y),-2pilexle2pithat are par...

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  10. Find the interval in which f(x)= 4x^3+3x^2+2x+1 is increasing.

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  11. A cubic f(x) vanishes at x= -2 and has relative minimum and maximum a...

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  12. Find the coordinates of the point on the curve y=x/(1+x^2)where the te...

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  13. Find the number of points of maxima and minima of the function. f(x)=1...

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  14. Find a point on the curve x^2+2y^2=6 whose distanced from the line x+y...

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  15. Prove that for any two numbers x1 and x2.(2e^(x1)+e^(x2))/3gte^((2(x1)...

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  16. If |f(x2)-f(x1)|le(x2-x1)^2AAx1,x2inR, then the equation of tangent to...

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  17. If y = f(x) = (x+2)/(x-1) then

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  18. A wire of length 2 units is cut into two parts which are bent respecti...

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  19. Consider f(x)=tan^-1(sqrt((1+sinx)/(1-sinx)),x in(0,pi/2). A normal to...

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  20. The line y=x+lambda is tangent to the ellips 2x^2+3y^2=1 Then lambda i...

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