Prove that the function ax+b f(x)= cx+d is constant (takes the same value for every x such that cx+d ‡0) if and only if a b=0. (Hint: Find the derivative of ƒ(x).)

Consider the following. 2x f(x) x + 2 Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. O y y 2- 0 --2 0 -1- 1 1 2 f(x) f(x) 2 3 3 X 4 O f' is never zero. O f approaches √2 when f' is zero. Of approaches -√2 when f' is zero. 4 5 f'(x) f'(x) 5 0 -1- Describe the behavior of the function when the derivative is zero. Of approaches to when f' is zero. O 3¹¹f'(x) 0.5 3 f'(x) 0 0.5 1 to X 2 1.5 2 X 2.5 f(x) f(x) 2.5 3

Please don't provide handwritten solution....

EXERCISE 2: Obtain the derivative of the following functions by applying the corresponding formula, then evaluate at -1