Consider the following. f(x) = 4x x+5 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. y 2- 07 -1- -2 0.5 O 3¹¹f'(x) 3 1 15 X f(x) y Of approaches ∞ when f' is zero. Of approaches -√2 when f' is zero. O f' is never zero. 2- 0 -1 Describe the behavior of the function when the derivative is zero. O f approaches √2 when f' is zero. --2 1 2 f(x) 3 f'(x) 2- f(x) f'(x) K f 0 0 1 2 3 4 5 0.5 1 1.5 2 3 4 5 f'(x) f(x) 2.5 3

Q7- Find the third derivative of the function

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The pounds of bananas sold each week at all Metro Seattle Albertsons stores as a function of price, p , in dollars/pound(lb.) is given by q(p) = 100e7.5-1.5p1. Express the Revenue function in terms of p and then find both the first and second derivatives of the revenue function. Type each of these in your text box, using appropriate standard mathematical formatting notation (like that shown above) in Excel. 2. Use Excel over an interval of [0, 6] in increments of .25 to create values for all 3 of your functions from part 1. This is hard! You should be getting the beginning values shown on the next page. Keep at it until you do!! You must create these values by typing in and using the correct formulas. 3. Use Excel to determine exactly where there are any Maximum and/or Minimum values for Revenue. In your text box, explain fully and completely how you determine where to look, and how you know from the First Derivative Test that you have a maximum or a minimum value. 4. Write a…

Find the derivative

Plz explain. Thanks

> Use the derivative to explain why the function f(x) = x +x³ is a one to one function.

Differentiate the function   f(x) =    5  - 1 /x

4

Consider the function f and its derivatives below. f'(x) = -2(2³-32) (³+64)² 6x²(³-128) (3+64)3 f"(x) = f(x) = 3 +64 Fill in the table below. For answers that require intervals, use interval notation and write your answer as a comma-separated list of intervals that are as inclusive as possible. Write "NONE" as your answer, if appropriate. Your answers must be exact or accurate to two decimal places. 2 1.26 38=2 4 1.59 16 2.51 √32 3.17 equations of vertical asymptote(s) of f: equations of horizontal asymptote(s) of f: f is decreasing on: f is increasing on: z-coordinate(s) of each local minimum of f: z-coordinate(s) of each local maximum of f: f is concave down on: f is concave up on: 01 x-coordinate(s) of each inflection point of f: √64=4 128 5.04 Sin den Ja