Lesson 4 6 Summary of Curve Sketching With

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Lesson 4 -6 Summary of Curve Sketching With Calculators

Lesson 4 -6 Summary of Curve Sketching With Calculators

Quiz • Homework Problem: MVT & Rolle’s 4 -2 Verify Rolle’s Theorem applies and

Quiz • Homework Problem: MVT & Rolle’s 4 -2 Verify Rolle’s Theorem applies and find all c’s f(x) = -x³- 3 x² + 2 x + 5 on [0, 2] • Reading questions: – What is an oblique asymptote called? – What is f(x) called if f(-x) = -f(x) for all x?

Objectives • Sketch or graph a given function using your calculator to help you

Objectives • Sketch or graph a given function using your calculator to help you

Vocabulary • None new

Vocabulary • None new

Graphing Checklist Domain – for which values is f(x) defined? Division by 0 or

Graphing Checklist Domain – for which values is f(x) defined? Division by 0 or negatives under even roots x -intercepts – where is f(x) = 0? y -intercepts – what is f(0)? Type in solve(f(x)=0, x) Type in f(x) | x = 0 Symmetry Even functions y-axis – is f(-x) = f(x)? Origin – is f(-x) = -f(x)? Odd functions Period – is there a number p such that f(x + p) = f(x)? Trig functions Asymptotes Horizontal – does or exist? Limit as x→±∞ Vertical – for what is ? F 3, limits Type in Lim(f(x), x, a) Division by 0 (and not removed by canceling)

Graphing Checklist (cont) Derivative Information: F 3 dif(f(x), x) Copy derivative and paste into

Graphing Checklist (cont) Derivative Information: F 3 dif(f(x), x) Copy derivative and paste into solve(f’(x)=0, x) Critical numbers – where does f’(x) = 0 or DNE? Increasing – on what intervals is f’(x) ≥ 0? Type in f’(x) | x = value Decreasing – on what intervals is f’(x) ≤ 0? Local extrema – what are the local max/min? Use f’ or f’’ test. 2 nd DT: Type in f’’(x) | x = critical # F 3 dif(f’(x), x) Copy derivative and paste into solve(f’’(x)=0, x) Concavity Up – where is f’’(x) > 0? Type in f’’(x) | x = value Down – where is f’’(x) < 0? Inflection points – where does f change concavity? Use calculator to check your info by graphing the function. Be Careful: the small screen can lead to some tricky views

Example 1 1 Graph -------x² – 4 Domain: f’(x) = -2 x/(x² - 4)²

Example 1 1 Graph -------x² – 4 Domain: f’(x) = -2 x/(x² - 4)² f’’(x) = 2(3 x² +4)/(x² - 4)³ x≠± 2 x –intercepts: None, y ≠ 0 y –intercepts: y = -1/4 Symmetry: Y-axis: Yes Origin: No Asymptotes H: y = 0 Critical numbers: Periodic: No V: x = -2, 2 x=0 Increasing: x<0 Decreasing: x>0 Max/Min: At x = 0, y = -1/4 is a relative max Concavity Up: |x|>2 Down: |x| < 2

Example 1 Graph y x

Example 1 Graph y x

Summary & Homework • Summary: – Calculator is a great tool that can help

Summary & Homework • Summary: – Calculator is a great tool that can help you with many things • • Derivatives Solutions to Equations Function zeros Functions evaluated at specific values – Because of its small screen it can trick us to seeing something that isn’t really there • Homework: – pg 330 -331: 1, 4, 12, 15, 16