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Unformatted text preview: Calculus I - Deﬁnition of __t_he Derivative
I The derivative off at x is given by The Derivative
L—r, v. .9 a. f’(x) = ”To “X + h}: ‘ ﬁx) Calculus I provided the limit exists. How do we use that weird § Common N9tation “2% deﬁnition? All of these really do mean the same thing.
Namely, the derivative of y with respect to x. f'(X) y' dy d
a a [f(X)] Dxb’] % Example __ 31%? Differentiability vs. Continuity . Find an equation of the tangent line at - If f is differentiable at x=c, then f is
the point where x = 2 on the graph of continuous at x=c. the function f(x) = «1x +1 - The converse is not true! It is possible
for a function to be continuous at x=c and not be differentiable at x=c.
. Example: Our friend f(x) =|x| . The Derivative Calculus I Spotting Those Problem - How can you tell by looking at the
graph of a function where it is not differentiable? - Places where the graph has “sharp points” . Places where the function is not continuous
. Vertical Asymptotes
. Finite Jumps The Derivative ...
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- Spring '11