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Given the function y = f(x) = x2.

a) From the graph of the function y = f(x) (Figure 4), indicate the increasing and decreasing intervals of the given function.

b) Calculate the derivative of f'(x) and examine the sign of f'(x).

c) From there, comment on the relationship between the increasing and decreasing intervals of the function and the sign of f'(x).
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 Jun 12, 2025
 #1
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a)  increases on   (0, inf)

     decreases on  (-inf, 0)

 

b)  derivative =  2x

 

c)  sign on f'(x) from (-inf, 0)  =  -

     sign on f'(x) from (0, inf) = +

 

cool cool cool

 Jun 20, 2025

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