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Sketch the graph of f(x) =x(1-x) over[0,1] . Refer to the graph and, without making any computations, find:

a. The average rate of change over [0,1]

b. The instantaneous rate of change at x=1/2

c. The values of days at which the rate of change is positive.

Can someone help me? I need step by step directions.

Sagot :

[tex]f(x)=x(1-x)\\\\zeros:x=0\ and\ x=1\\\\vertex\ (x_v;\ y_v):\\\\x_v=\frac{0+1}{2}=\frac{1}{2}\\\\y_v=\frac{1}{2}(1-\frac{1}{2})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]


[tex]a)\\\frac{f(0)-f(1)}{0-1}=0\\\\b)\\ROC_{inst}(\frac{1}{2})=0\\\\c)\\(0;\ \frac{1}{2})[/tex]
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