Finding the slope of a tangent line using the fourstep process
Definition of the Slope of a Tangent Line and Definition of the Derivative,
f’(x).
Finding the derivative of a function by use of the definition
Rules (Shortcuts) for finding Derivatives
Real World applications
Using the fourstep process, find the slope f the tangent line to the graph of the
function
f(x) = 7x
2
+9x 3
at any point.
. f(x+h)
2. f(x+h) – f(x)
3.
f(x+h) – f(x)
h
4.
lim
f(x+h) – f(x)
h →0
h
Find the slope of the tangent line to f(x) = 1/x at the point (3, 1/3)
{by the long way}
Write an equation of the tangent line
Derivative Rules:
Rule 1: The Derivative of a Constant
If f(x) = c,
Then f ’(x) = 0.
(If a function is constant, its instantaneous rate of change is zero, i.e. – it
doesn’t change.)
Rule 2: The Power Rule
If f(x) = x
n
for any real number n,
Then f ’(x) = n x
n 1
.
Rule 3 The Derivative of a constant times a function Is the constant times the
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 Spring '08
 VAUGHN
 Calculus, Derivative, Slope

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