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 is differentiable for all x and that f'(x) le2" for all "x," If "f(1)=2 and f(4)=8 , then f(2)has the value equal to ……….. .

Suppose that f is differentiable for all x and that f'(x) le2" for all "x," If "f(1)=2 and f(4)=8 , then f(2)has the value equal to ……….. .

Suppose that f is differntiable for all x such that f'(x)le2 for all x, If f(1)=2 and f(4) =8 , then f(2) has the least value equal to

If function f(x) = x-|x-x^(2)|, -1 le x le 1 then f is

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) ?

Show that the function f (x) = {{:( x , if x lt 1), ( 3-x , if 1 le x le 3), (x ^(2) - 4x +3, if x gt 3):} is not differentiable at 1,3.

Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x le 3), ( x ^(2) - 4x + 3, if x gt 3):} is not differentiable at x = 1,3