Analyze using the tools of Calculus and sketch the graph of x3-1 f(x) = Otherwise write “none." Use exact values where possible. Show all steps when calculating derivatives and applying the First and/or Second Derivative Tests. There must be an answer for all categories. x3+1 Second Derivative: Intervals of Concave Up: Intervals of Concave Down: Inflection Points:

Find all relative extrema of the function. Use the Second Derivative Test where applicable. f(x) = (x + 9)2

Use the definition to find the derivative of f(E) 2t+1 t+3 (You need to show your work in details to get full credits) Edit View Insert Format Tools Table

On the previous page, we learned how to use the graph of a function to determine where the function is NOT differentiable. At any given input value, a function is either differentiable or not differentiable. Consequently, it is often easier to first determine where a function is not differentiable, and then identify the intervals where the function is differentiable. arch Below is a graph of the function y = f(x). Determine where the function is differentiable. Explain your reasoning and write your answer in interval notation. f3 #M 3 10 12 D 9 + E DO 8 7 6 5 4 3 2 O $ 4 1 2 81 R F f5 ur do % 5 3 T G 4 f6 6 5 f7 Y 6 7 8 H y = f(x) & 7 fg 89 U 8 J hp fg 10 X 1 9 K h f10 4 f11 L P f12 + [ insert prt sc