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I just read the chapter on Tangent Lines and Slopes. I did a problem, double-checked the math, then turned to the back of the book and found out the answer was completely incorrect. I retraced again, and found no problem, but the book is a bit confusing so I might have missed something.

The problem reads: Find a formula that gives the slope at any point P (x,y) on the given curve. [itex]y=4-x^2[/itex] [itex]P:(1,-1)[/itex]

My work is as follows:

1)I begin by making a secant line from point P to a point Q, which I arbitrarily place. The coordinates are [itex]Q:(-1+\Delta x, 4-(-1+\Delta x)^2[/itex]

2)To find my slope: [tex]\frac{\Delta y}{\Delta x} = \frac{4-(-1+\Delta x)^2}{\Delta x}[/tex]

3)This becomes: [tex]\frac{4-1+2\Delta x-\Delta x^2}{\Delta x}[/tex]

4)Finally, I get [itex]5-\Delta x=m[/itex] Getting rid of the [itex]\Delta x[/itex] my slope is [itex]m=5[/itex]

The back of the book says the answer is -2x.

What happened?