BC Flashcards
Average Rate of Change
Slope of secant line between two points, use to estimate instantanous rate of change at a point.
Instantenous Rate of Change
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
Product Rule
uv’ + vu’
Quotient Rule
(uv’-vu’)/v²
Chain Rule
f ‘(g(x)) g’(x)
y = x cos(x), state rule used to find derivative
product rule