13112an3.1-3

# 13112an3.1-3 - c Kendra Kilmer February 3 2012 Section 3.1...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

### Page1 / 3

13112an3.1-3 - c Kendra Kilmer February 3 2012 Section 3.1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online