Question

Solution

Correct option is

1/2

Clearly f (x) is continuous and differentiable on (0, 1) for α > 0.

Also, f (0) = 0 = (1)

For f (x) to be continuous at x = 0, we must have  So, f (x) is continuous at x = 0 for α > 0.

∴ By Rolle’s theorem can be applied on f (x) in [0, 1] for all α > 0

SIMILAR QUESTIONS

Q1

x and y are the sides of two squares such that y = x – x2. Find the rate of change of the area of the second square with respect to the first square.

Q2

Find equation of tangent to the curve 2y = x2 + 3 at (x1y1).

Q3

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

Q4

Find the sum of the intercepts on the axes of coordinates by any tangent to the curve, Q5

The tangent represented by the graph of the function y = (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, Q6

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.

Q7

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

Q8

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.

Q9 in which interval

Q10

If abc be non-zero real numbers such that  Then the equation ax2 + bx + c = 0 will have