| The derivative is the slope of the equation line at any given point. | ||
| When the derivative is positive, the graph is going up. | ||
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| When the slope is a negative number, the graph is going down. | ||
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| When the slope is zero, the graph is horizontal. | ||
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| What would we do if we had something like: | ||
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F(X) = X2 |
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| Since we're calculus big shots now, | ||
| We would find the derivative of this, | ||
| in our heads!... | ||
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F'(X) = 2X |
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| So the derivative is negative when X is less than zero: | ||
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| the derivative is zero when X = 0: | ||
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| the derivative is positive when X is greater than zero. | ||
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| So from this information, | ||
| we know that the graph of F(X) = X 2 looks something like this: | ||
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| If we solve the equation for the point where the slope is zero | ||
| (where X = 0 in this particular case), we can tack this curve to a coordinate axis: | ||
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| The slope can only change directions | ||
| (like going from positive to negative or negative to positive), | ||
| if there is a point where the slope is zero or undefined in between. | ||
| That's what happened when X = 0 in this problem. | ||
| If you have an equation where the slope is never zero or undefined, | ||
| it will either always be going up or always be going down. | ||
| One more point: | ||
| The slope CAN change directions where the slope is zero or undefined, | ||
| but it doesn't have to. | ||
| Wouldn't it be nice to have a test to know if it does change directions | ||
| without drawing the graph first? | ||
| OK, here's another question: | ||
| Guess what's on the next page? | ||
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copyright 2008 Bruce Kirkpatrick |