Document 10435102

MATH 131-505 Spring 2015
Review II
• know how to interpret the average rate of change and instantaneous rate of change on graphs
(as shown on page 1)
• know the slope of the tangent line is the same as the derivative of f (x) at x = a, i.e. f 0 (a)
• given a graph f (x), be able to graph f 0 (x)
• know when f (x) fails to be differentiable
• be able to use the limit definition to find f 0 (x)
• know the definitions of local maximum and local minimum
• know everything on page 1 from the notes and be able to use it (to get all information about
f (x) from f 0 (x)), i.e. problem 3 on page 2
• be able to interpret f 0 and f 00 , like problem 2
• be able to find the derivatives using the rules listed on page 1
• be able to find the equation of tangent line that is parallel to a given line or to find the equation
of the normal line.
• know where a tangent line is horizontal
3.2: be able to find the derivatives using the product rule and quotient rule
• know how to find the derivative of trig functions
• know how to find the tangent line at a point to a curve
3.4: know how to use chain rule to find the derivatives
3.7: know the formula on page 1 and use it to find the derivatives
• given a distance/position function s(t), know the velocity v(t) = s0 (t) and the acceleration
a(t) = v 0 (t)
• be able to analysis the motion of a particle if s(t) is given
3.9: know how to use linearization to approximate a number
review quizzes/notes
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