Difference between revisions of "Math 22 The Derivative and the Slope of a Graph"

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Example: Find the Different Quotient of  
 
Example: Find the Different Quotient of  
  
'''1)''' <math>f(x)x^2-1</math>
+
'''1)''' <math>f(x)=x^2-1</math>
  
 
Solution: Consider <math>\frac {f(x+h)-f(x)}{h}=\frac{(x+h)^2-1-(x^2-1)}{h}</math>
 
Solution: Consider <math>\frac {f(x+h)-f(x)}{h}=\frac{(x+h)^2-1-(x^2-1)}{h}</math>

Revision as of 15:15, 5 October 2020

Slope of a Graph

We can estimate the slope at the given point to be


Slope =

Difference Quotient

 The slope  of the graph of  at the point  can be 
 written as :
 
 
 
 The right side of this equation  is called Difference Quotient

Example: Find the Different Quotient of

1)

Solution: Consider

2)

Solution:  
Consider

Definition of the Derivattive

 The derivative of  at  is given by
 
 
 
 provided this limit exists. A function is differentiable at  when its 
 derivative exists at . The process of finding derivatives is called differentiation.

Example: Use limit definition to find the derivative of

1)

Solution: Consider:

2)

Solution:  
Consider:

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