MAC 2233 Chapter Notes - Chapter 2: Riemann Sum, Quotient Rule, Intermediate Value Theorem
16 Oct 2018
School
Department
Course
Professor
Document Summary
If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. Slope of secant line between two points, use to estimate instantanous rate of change at a point. Slope of tangent line at a point, value of derivative at a point. Formal definition of derivative limit as h approaches 0 of [f(a+h)-f(a)]/h. Alternate definition of derivative limit as x approaches a of [f(x)-f(a)]/(x-a) When f "(x) is positive, f(x) is increasing. When f "(x) is negative, f(x) is decreasing. When f "(x) changes from negative to positive, f(x) has a relative minimum. When f "(x) changes fro positive to negative, f(x) has a relative maximum. When f "(x) is increasing, f(x) is concave up. When f "(x) is decreasing, f(x) is concave down. When f "(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a point of inflection. When is a function not differentiable corner, cusp, vertical tangent, discontinuity.
