Geometrical Interpretation Of The Derivative
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Geometrical Interpretation of The Derivative
Geometrically, the derivative of a function f (x) at a point x = c represents the slope of the tangent to the curve y = f (x) at (c,f (c)).
Let y = f (x) be differentiable on an open interval containing c. Let p (c,f (c) ) and Q (c+h) be two neighboring points on the graph of y = f (c). Then the slope of the secant line PQ is f (c+ h) - f(c) Since
h
the tangent at P is a limiting position of secant lines PQ, the slope of the tangent at P is the limiting value of the slope of the secant lines as Q approaches P. But as Q approaches p, h → 0.
The slope of the tangent at P
= lim f (c+ h) - f(c)
h
= f ’(c).
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Let y = f (x) be differentiable on an open interval containing c. Let p (c,f (c) ) and Q (c+h) be two neighboring points on the graph of y = f (c). Then the slope of the secant line PQ is f (c+ h) - f(c) Since
h
the tangent at P is a limiting position of secant lines PQ, the slope of the tangent at P is the limiting value of the slope of the secant lines as Q approaches P. But as Q approaches p, h → 0.
The slope of the tangent at P
= lim f (c+ h) - f(c)
h
= f ’(c).
For more help in Geometrical Interpretation of The Derivative click the button below to submit your homework assignment