251- Difference Quotient PDF

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How to do Difference Quotient and some example of it...

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Math 251 – Calculus 1 Handout – Difference Quotient Practice

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f (x + h) ! f (x) is called a difference quotient and has important uses in the study of h calculus. The example below illustrates a step-by-step process for evaluating a difference quotient. The quantity

2 Example: Given the function f (x) = 3 ! 2x , find and simplify the difference quotient

f (2 + h) ! f (2) . h

Step 1: Find and simplify f (2 + h) . 2

f (2 + h) = 3 ! 2(2 + h)

= 3 ! 2(4 + 4h + h 2 ) = 3 ! 8 ! 8h ! 2h2 = !5 ! 8h ! 2h2

Step 2: Find and simplify f (2 + h) ! f (2) .

f (2 + h) ! f (2) = ( !5 ! 8h ! 2h 2 ) ! (3 ! 2(2)2 ) = !5 ! 8h ! 2h2 ! (!5) = !8h ! 2h2 Step 3: Find and simplify

f (2 + h) ! f (2) . h

2 f (2 + h) ! f (2) = !8h ! 2h h h h(!8 ! 2h ) = h = !8 ! 2h

Exercise: Find and simplify the difference quotient 1) f (x) = 2 ! 3 x

f (2 + h) ! f (2) for each of the following functions. h

2) f (x) = x 2 ! 4

3) f (x) = 5

f (x + h) ! f (x) for each of the following functions. h 1 5) f (x) = x 2 ! 2x + 5 6) f (x) = x

Exercise: Find and simplify the difference quotient 4) f (x) = 5x ! 4

7) f (x) = x Hint: To simplify, rationalize the numerator of the expression by multiplying by an expression involving the conjugate. 1/12/13ss...