Suppose that for a function `f(x),f'(x)le1" for all "1lexle4`. Show that `f(4)-f(1)le3`.

Suppose that for a function f(x), f(x) le 1 for all 1 le x le 4 . Show that f(4)-f(1) le 3

Suppose that f(0) = -3, and f' (x) le 5 for all values of x how large can f(2) possibly be?

The diagram shows the graph of the derivative of a functin f(x) for 0 le x le 4 with f(0) = 0. Which of the following could be correct statements for y = f(x)? (a) Tangent line to y = f(x) at x = 0 makes an angle of sec^(-1) sqrt 5 with the x - axis. (b) f is increasing in (0, 3). (c) x = 1 is both an inflection point and the point of local extremum. (d) Number of critical point on y = f(x) is two.

Suppose f is a real function satisfying f(x+f(x))=4f(x)a n df(1)=4. Then the value of f(21) is 16 21 64 105

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Suppose f(x) is a differentiable function for all x with f'(x) le 29 and f(2) =17 . What is the maximum value of f (7) ?

Suppose the function f(x)-f(2x) has the derivative 5 at x =1 and derivative 7 at x = 2. The derivative of the function f(x)-f(4x) at x = 1, has the value equal to

Find the range of the function f(x) = [ 2 x ] , 1/3 le x le (8)/(3)

Suppose that f is even, periodic function with period 2, and that f(x) = x for all x in the interval [0, 1]. Then draw the graph of y = f(x).