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The tangent to the graph of the function `y=f(x)` at the point with abscissa `x=a` forms with the x-axis an angle of `pi/3` and at the point with abscissa `x=b` at an angle of `pi/4`, then the value of the integral, `int_1^b f'(x).f'' (x) dx` is equal to

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MOTION-TANGENT & NORMAL-EXERCISE 3
  1. If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , t...

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  2. The tangent at a variable point P of the curve y = x^2 – x^3 meets it ...

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  3. Find the points on the curve y=x^3 at which the slope of the tan...

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  4. Show that for any point of the curve x^2 - y^2 = a^2 the segment of th...

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  5. Prove that the length of segment of all tangents to curve x^(2/3)+y^(2...

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  6. find the abscissa of the point on the curve xy=(c-x)^2 the normal at ...

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  7. The angle of intersection of the curves y =2 sin^2 x and y = cos 2 x ...

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  8. if two curves C1 : x=y^2 and C2 : xy=k cut at right angles,then value ...

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  9. A particle moves along the curve 6y = x^(3)+2. Find the points on th...

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  10. The length x of a rectangle is decreasing at the rate of 3 cm/minute ...

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  11. The length x of rectangle is decreasing at a rate of 3 cm//min and wi...

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  12. A lamp is 50ftdot above the ground. A ball is dropped from the same he...

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  13. A man 1.5 m tall walks away from a lamp post 4.5 m high at a rate of 4...

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  14. A man 1.5 m tall walks away from a lamp post 4.5 m high at a rate of 4...

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  15. The tangent to the graph of the function y=f(x) at the point with absc...

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  16. The set of values of p for which the equation |ln x| -px = 0 possess t...

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  17. Find the minimum value of (x1-x2)^2+(sqrt(2-x1^2)-9/(x2))^2 where x1...

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  18. The number of solutions of the equation |f(|x|))| – 3 = 0

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  19. The equation of the normal to the curve y^(4)=ax^(3) at (a,a) is

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  20. The equation of tangent at Q is

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