Find C Of The Lagrange’s Mean Value Theorem For Which

Find the equation of tangent to the curve y² = 4ax at (at², 2at).

Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,  

The tangent represented by the graph of the function y = f (x) at the point with abscissa x = 1 form an angle π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle π/4. Then find the value of,  

Three normals are drawn from the point (c, 0) to the curve y² = x, show that c must be greater than ½. One normal is always the x-axis. Find c for which the other normals are perpendicular to each other.

Find the acute angle between the curves y = | x² – 1| and y = | x² – 3 | at their points of intersection when x > 0.

If the relation between subnormal SN and subtangent ST at any point S on the curve; by² = (x + a)³ is p(SN) = q(ST)², then find the value of p/q. 

 in which interval

If f (x) = x^α log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is:

If a, b, c be non-zero real numbers such that  

Then the equation ax² + bx + c = 0 will have

Let f (x) and g (x) be differentiable for 0 ≤ x ≤ 2 such that f (0) = 2, g(0) = 1 and f (2) = 8. Let there exists a real number c in [0, 2] such that f’(c) = 3g’(c) then the value of g(2) must be: