UWPC Chap 5 Difference Quotient (DQ) Worksheet PDF

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The topic is on difference quotient it gives example and explanations...

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UW Pre-Calculus Name: ______________ Difference Quotient (DQ) Worksheet 19.Mar.22 2 Find the DQ for: f ( x) =x - 4 x+ 3

Step 1: calculate f ( x + h) with excellent algebra Step 2: subtract f(x) from the answer to Step 1 Step 3: divide the answer to Step 2 by h 2

Step 1: f ( x + h) =( x+ h) - 4 ( x+ h) + 3 =x2 + 2xh + h2 - 4x - 4h+ 3 - f ( x) =- ( x2 - 4 x+ 3) =- x2 + 4 x- 3

x2 + 2xh + h2 - 4x- 4h+ 3 - x2 + 4x- 3 2 The answer to Step 2 is: =2xh + h - 4h

2xh + h2 - 4h =2x+ h- 4 h Step 3: When you divide by h, you get: Practice: A. Given: f ( x) =4 x , find the following and simplify. 2

a) f ( x + h) b) f ( x + h) - f ( x) f ( x + h) - f ( x)

h c) d) If h = 0, what is the resulting answer to part (c).

f ( x) = B. Given: e) f ( x + h)

1 3x2 , find the following and simplify.

UW Pre-Calculus Name: ______________ Difference Quotient (DQ) Worksheet 19.Mar.22 f) f ( x + h) - f ( x) f ( x + h) - f ( x) h g) C. Now you do it: For Test before Thanksgiving, problems 1 to 5 are necessary For the final exam ALL problems will be considered.

f ( x + h) - f ( x) h Find the for: 2 1. f (x) =x - 5x - 1

f (x) = 2.

5 x

2 3. f (x) =5x - 2x

2 4. f (x) =17x - 13x

2 5. f (t) =- 16t + 9t +10

f ( 2 + h ) - f ( 2) h 6. Given: f (x) =3x - 5x +1 , find 2

f (x) = 7. Given:

1 f ( 0.01+ h) - f ( 0.01) x , find h

UW Pre-Calculus Name: ______________ Difference Quotient (DQ) Worksheet 19.Mar.22 g( x + h) - g( x) h 8. Given: g(x) = x , find

2

9. Given: g(x) =3 ( x - 4 ) - 11 , find

g( a + h) - g( a) h...