Question

Suppose f is differentiable on R and a ≤ f’(x) ≤ b for all x ∈ R where ab> 0. If f (0) = 0, then

Solution

Correct option is

ax ≤ f (x) ≤ bx

For x > 0. Applying Lagrange’s theorem on [0, x] we have c ∈ (0, x) such that

                          

  

x > 0, similarly for x < 0 applying lagrange’theorem for [x, 0], we have ax ≤ f(x) ≤ bx.

SIMILAR QUESTIONS

Q1

The tangent to the curve 

At the point corresponding to  is

Q2

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are

Q3

 the in this interval

Q4

The set of all values of a for which the function

                   

decreases for all real x is

Q5
Q6

The length of a longest interval in which the function 3 sin x – 4Sin3x is increasing is

Q8

The equation e 1 + x – 2 = 0 as 

Q9

The function f satisfying 

Q10

The minimum value of (x) =