2. Graph the function f (x)and its derivative in the window x2+1 [-3,3] by [-1,1

Question

2. Graph the function f (x)and its derivative in the window x2+1 [-3,3] by [-1,1 Now answer the same set of questions as in # 1 above: a·Over what intervals does the graph of/appear to be rising as you move from!eft to right? b. Over what intervals does the graph of f 'appear to be above the x-axis? c. Over what intervals does the graph of fappear to be falling as you move from left to right? d. Over what intervals does the graph of f" appear to be below the x-axis? e. What are the x-coordinates of all of the peaks and valleys of the graph of f? f. For what values of x does the graph of f ' appear to meet the x-axis? 3. On the basis of your experience so far, write a statement (or statements) about properties you have observed about the graph of its derivative. a. How is the graph of the derivative when a function is rising? b. How is the graph of the derivative when a function is falling? c. What happens to the graph of the derivative when a function has a peak or a valley?

Explanation / Answer

3.

a. When a function is rising, then derivative of function is positive. So graph of derivative is above x-axis when a function is rising.

b. When a function is falling, then derivative of function is negative. So graph of derivative is abelow x-axis when a function is falling.

c.

When function has a peak or a valley i.e. its local maxima or local minima then derivative of function changes its sign and at that point derivative = 0

That means graph cut or touches x-axis when function has a peak or a valley

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