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

2 le 3x -4 le 5

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

Solve 1 le |x-2| 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.

Draw the graph of the function f(x ) = {{:(1+x , -1 le x le 0),( 1-x, 0 lt x le 1):}

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) ?

Verify Rolle's theorem for the funnction f(x) = 4x^(3) - 9x " in " -(3)/(2) le x le (3)/(2)

Using Rolle's theorrem find c if f(x) = (x-a) (b-x) , a le x le b a ne b