121616949-math.37

121616949-math.37 - 2.1 The slope of a function 23 which is...

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2.1 The slope of a function 23 which is the slope of a line, then we figure out what happens when Δ x gets very close to 0. We should note that in the particular case of a circle, there’s a simple way to find the derivative. Since the tangent to a circle at a point is perpendicular to the radius drawn to the point of contact, its slope is the negative reciprocal of the slope of the radius. The radius joining (0 , 0) to (7 , 24) has slope 24/7. Hence, the tangent line has slope - 7 / 24. In general, a radius to the point ( x, 625 - x 2 ) has slope 625 - x 2 /x , so the slope of the tangent line is - x/ 625 - x 2 , as before. It is NOT always true that a tangent line is perpendicular to a line from the origin—don’t use this shortcut in any other circumstance. As above, and as you might expect, for different values of x we generally get different values of the derivative f ( x ). Could it be that the derivative always has the same value?
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