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:
As f (x) and g(x) are continuous and differentiable in [0, 2], then there exists at least one value ‘c’ such that
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) = xα 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
Find c of the Lagrange’s mean value theorem for which
If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then is equal to: