Section: Week 04: Sept. 13 | MAT 112A (Fall 2021) - Calculus I and Modeling | Davidson College

Section: Week 04: Sept. 13 | MAT 112A (Fall 2021) - Calculus I and Modeling | Davidson College

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  Expected Tues & Thurs 10:50 -- 11:50 a.m. Email Neidinger (rineidinger) if not working or to arrange any other time.
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Week 04: Sept. 13

Week 04: Sept. 13
- #10 Assignment
  Read 3.4
  Prob A. If f(x)=x, prove f '(x)=1 by definition of derivative.
  
  Prob B. If f(x)=x⁴, prove f '(x)=4x³ by definition of derivative (expand (x+h)⁴).
  3.4; 1, 15+, 17+, 38, 39, 55.
  On 15 and 17, in addition to everything instructed, after you prove the derivative formula, use it to find the equation of the tangent line to the curve at x=3.
- Differentiabul song URL
- Example: Derivative Definition with Square Root File
- #11 Assignment
  
  Read 3.5 and 4.1.
  3.5; 6, 7, 8, 9, 10, 12.
  4.1; 3, 12, 17, 20, 32.
  On 20: Rewrite as powers of x; don't use quotient rule.
- #12 Assignment
  
  Read 4.2.
  Prob A: If f(x) = c u(x), prove f '(x) = c u'(x) by definition of derivative.
  4.1; 43, 57, 58abcd, 62, 71. (Hints below; remember to include units in 62 and 71)
  4.2; 7, 19, 22, 29, 30, 33. (Instructions specify use product or quotient rule, so you must!)
  Hint for 4.1 probs: Easier not to use quotient rule, instead pull constants out front and/or use negative exponents.
  Hint on 56d: Units of BMI are just that, units of BMI. Describe the derivative as how much something changes for every what?
  Optional star (hand in separately within a week): do the pair of problems *(4.1;65 and 4.2;37 ).