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Calculus: Ch. 2.4-3.2 (the derivative)
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*The derivative of f(x) at x=a is defined as
(Except replace the x in parentheses with an a)
IF THE LIMIT EXISTS!!!
*The derivative of f(x) at x=a is often denoted by ________ or by __________
f'(a) or (df/dx) I x=a
*We can also write f'(a) as
limit delta x--> (delta f)/(delta x)
What is a line that intersects a curve at a point?
the tangent line
Where the derivative exists, it is _____________
differentiable
Where the function is differentiable on the whole set, say that the whole set is _____________
differentiable
*A function is _______________________ S if f'(a) exists for each as in S
differentiable on a set
*What is the linear approximation formula?
f(x) + hf'(x) ~= f(x + h)
*When h= delta x. we have
f(x + delta x) ~= f(x) + f'(x)delta x
*The differential of x is
dx = delta x
*the differential of f is
df = f'(x) dx or f'(x)delta x
*Since delta f = f(x + dx) - f(x), we can also write
delta f ~= df
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