Do not use technology. The figure below shows the graph of f', the derivative of f. The function f is a twice differentiable function on x E (-co, co), f'(-0.8) = 0, and f"(1.3) = 0. -3 (a) For what values of x is f increasing? (Enter your answer using interval notation.) (b) For what values of x is the graph of f concave downward? (Enter your answer using interval notation.)

A company's annual revenue after x years is f(x)=x²-9x² +15x +29 thousand dollars (for x 20). (a) Make a sign diagram for the first derivative Select Make a sign diagram for the second derivative. Soled Select (b) Sketch the graph of the revenue function, showing all relative extreme points and inflection points. 30 35 30 25 20 NANA 15 10 6 35 25 20 15) 10 (c) Give an interpretation of the infection point. 6 35 20 15 10 The decline in revenue first begins to slow at the inflection point. O The company reaches minimum revenue at the inflection point. O The increase in revenue first begins to slow at the inflection point. O The company reaches maximum revenue at the inflection point. Onone of these 4 2 35 25 20 15) 10 4

What information can be obtained from derivatives? Please provide 2 examples from the real world and explain the information that you could gain from it.

Which defines as the process of finding the derivative of a function? *

For the following graphical representation of a function ? (?):(1) Mark the points on the graph where the derivative is zero;(2) Show the regions where the function is increasing (positive derivative) and where it isdecreasing (negative derivative);(3) Sketch the first derivative ?′(?);(4) Repeat steps (1)-(3) on the derivative ?′(?) itself to sketch the second derivative ?′′(?).

How do you use the second derivative test to analyze concavity of a function?

Consider the following (a) Find an equation of the tangent line to the graph of the function at the indicated point. (Use x for the independent variable and y for the dependent variable.) (b) Use a graphing utility to graph the function and its tangent line at the point. Must solve this part as well (c) Use the derivative feature of a graphing utility to confirm your results. Show a work on part C such as graph and details Thanks

1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the derivative. 2. (#9 Exam 1 Review) Sketch the graph of the function g for which: g(0) = g(2) = g(4) = 0, g' (1) = g(3) = 0,g' (2) = -1, lim g(x) = ∞, and lim g(x) = -∞ x 5 x-1+ 3. State the three-part Definition of Continuity. 4. (#13 Exam 1 Review) The graph of f is given. State, with mathematically correct reasons, the values for which f is not differentiable. -2 VA 0 2 4 X (Description: Graph with three components. First component is horizontal line in the 2nd quadrant to x = -2. Sharp turn upwards in downward arc into the 1st quadrant and ends with open dot where x = 1. Second component is solid dot at x = 1 vertically below the open dot. Third component begins with open dot at x = 1 below the solid dot. The graph falls in downward arc shape into the 4th quadrant, takes a sharp turn at x = 3 and continues as…