1.Suppose f and g are continuos on [a,b] and differentiable on (a,b). Suppose also that f(a)=g(a) and the first derivative of f(x)<first derivative of g(x) for a<x<b. Prove that f(b)<f(b).
2.Suppose that 3 less than or equal to the first derivative of f(x), which is less then or equal to 5 for all values of x. Show that 18 is less then or equal to f(8)-f(2), which is less then or equal to 30. By MVT
3. A number a is called a fixed point to a function f if f(a)=a. Prove that if the first derivative of f(x) doesn't equal 1 for all real numbers x, then f has at most one fixed point
2.Suppose that 3 less than or equal to the first derivative of f(x), which is less then or equal to 5 for all values of x. Show that 18 is less then or equal to f(8)-f(2), which is less then or equal to 30. By MVT
3. A number a is called a fixed point to a function f if f(a)=a. Prove that if the first derivative of f(x) doesn't equal 1 for all real numbers x, then f has at most one fixed point
