Sketch y = x(4 - x) for x that is equal to or less than 0. Explain in words what happens to the slope of the curve as we move along it from left to right.

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- Feb 24th 2008, 10:24 AM #1

- Feb 24th 2008, 10:32 AM #2
## Make a table of values...

Since we are making a graph we can pick any values of x that we wish...

Since they ask us pick pick values less than or equal to zero that is a good place to start.

so lets start with x = 0, x= -1, x = -2, x = -3

$\displaystyle y=x(4-x)$

evaluating at the above values

$\displaystyle y=0(4-0)=0$ gives the point $\displaystyle (0,0)$

$\displaystyle y=-1(4-(-1)=0$ gives the point $\displaystyle (-1,-5)$

$\displaystyle y=-2(4-(-2))=0$ gives the point $\displaystyle (-2,-12)$

$\displaystyle y=-3(4-(-3))=0$ gives the point $\displaystyle (-3,-21)$

if we plot these ordered pairs and connect them with a smooth curve we should be able to answer the question.