What are the guidelines for analyzing the graph of a function?
1) Determine the domain and range of a function
2) Determine the intercepts, asymptotes, and symmetry of the graph
3) Locate the x values for which f'(x) and f"(x) either are zero or do not exist. Use the results to determine relative extrema and points of inflection
When analyzing a function, how do you find x and y intercepts?
Section P.1
Symmetry
P.1
Domain and range
P.3
Continuity
Section 1.4
Verticle Asymtotes
1.5
Differentiability
2.1
Relative extrema
3.1
Concavity
3.4
Points of inflection
3.4
Horizontal asymptotes
3.5
Infinite limits at infinity
Section 3.5
What are the guidelines for implicit differentiation?
1. Differentiate both sides of the equation 'with respect to x'. 'x' variables are differentiated normally but 'y' variables must use the chain rule
2. Collect all terms containing dy/dx [ or " y' "] on the left side of the equation and move all other terms to the right side of the equation.
3. Factor dy/dx of the side of the equation
4. Solve for dy/dx
What are the guidelines for implicit differentiation?
1) Differentiate both sides of the equation (with respect to x) - what does 'with respect to x' mean?
'respect to x' means 'x' variables are differentiated normally. 'y' variables use the chain rule
2) Collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation. (all the primes [y'] on one side, everything else on the other)
3) Factor dy/dx [y'] out of the left side of the equation