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Graded Worksheet on Definition of Derivative

MAT 1161

Sean Forman

January 30, 2004

Due February 3, 2004

1. Find $f'(x)$ using the definition of the derivative. $f(x) = 9x -8$.

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

2. Find $f'(x)$ using the definition of the derivative. $f(x) = 8x^2 - 3x + 12$.

3. Find $${\lim_{x \to 3} \frac{x^2 - 5x + 6}{x^2 - 3x}}$$.

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

4. An automotive dealership finds that the number of cars it sells on day $x$ of an advertising campaign is $S(x) = -x^2 + 10x$ (for $0 \leq x \leq 7$). $S'(x) = -2x + 10$.
   • What does $S'(x)$ mean and what are its units?

   • What is $S'(3)$ and what does that mean?

   • When does the number of people buying cars begin to decrease?