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**Unformatted text preview: **c Kendra Kilmer February 3, 2012 Section 3.1 - Derivatives of Polynomials and Exponential Functions
Constant Function Rule: If f (x) = c where c is a constant then Power Rule: If f (x) = xn , where n is a real number, then Constant Multiple Property: If f (x) = k · g(x), where k is any real number, then Sum and Difference Property: If h(x) = f (x) ± g(x) where f and g are both differentiable functions, then Example 1:Differentiate the following functions:
a) f (x) = 3 b) f (x) = e c) f (x) = √
5 8 d) f (x) = x4 e) f (x) = x1/2 f) f (x) = g) f (x) = √
3 x5 5
x2 h) y = 3x2 + 7x − 9 1 c Kendra Kilmer February 3, 2012 i) m(t ) = √ j) k(x) = x3 + 4x2 − 17 + x
x k) y = 5t − t 1/2 + e 3x2 + x4
√
5x Example 2: If a book is dropped from a building 400 feet tall, its height above the ground (in feet) after t seconds
is given by s(t ) = 400 − 16t 2
a) Compute s′ (t ) and interpret. b) Compute s(2) and s′ (2) and interpret. c) When does the book hit the ground? d) What is the impact velocity? 2 c Kendra Kilmer February 3, 2012 Example 3: If f (x) = 3x4 − 2x2 , where does the graph of the function have a horizontal tangent line? Derivatives of Exponential Functions
• If f (x) = bx then
• If f (x) = ex then
Example 4: Find the derivative of each of the following functions:
a) f (x) = 2ex
b) f (x) = 7(5)x Example 5: The resale value R (in dollars) of a company car after t years is estimated to be given by
R(t ) = 20000(0.86)t
What is the rate of depreciation (in dollars per year) after 1 year? 3 years? Section 3.1 Highly Suggested Homework Problems: 3, 7, 11, 15, 19, 23, 27, 31, 41, 45, 47, 49, 53, 65 3 ...

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