Jen%20Gulya

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Derivatives
By Jenn Gulya
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The derivative of a function f with respect to
the variable is the function f whose value at
x, if the limit exists, is
This value is, also, representative of the slope
of the function at a point.
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When f'(a) doesn't exist.
Where a is an x value, F(a) must be
differentiable for f(a) to exist. So at some
points a derivative may not exist.
(An example would be the absolute value graph,
which lacks a derivative at x0).
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Rules of Differentiation
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Example 1
Y x36x2-(5/3)x16 Applying Rules 1 through 4,
differentiate the polynomial term-by-term
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Graph of original Function
It can be seen that when the original curve
levels off and changes direction the graph of f
crosses the x-axis.
Graph of derivative
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Example 2
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When the calculated derivative and NDER of the
function on the calculator are graphed together.
They appear to be identical, which is a strong
indication that the calculation is correct.
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Jenn Gulya
Will be majoring in Biology at Rutgers University
in the Fall.