4/5 math terms

English	Photos
Orthogonal Curves are	At points of intersection of the curves, the tangent lines are perpendicular.
Intermediate Value Theorem	If f(x) is continuous on [a,b] and f(a) ≠ f(b) then There is a "c" inside (a, b) such that f(c) = N where N is between f(a) and f(b)
Differential dy =
f(x) is CONTINOUS at x = a if 1) 2) 3)
Instantaneous Rate of Change	f ' (a)
Definition of an EVEN function (cos x is even)	f(x) = f(-x)
If f(x) is differentiable at x = a , is f(x) continuous at x = a ? Vice versa?	Yes Not necessarily (Ex- peaks)
Definition of an ODD function (sin x is odd)	f(-x) = - f(x)
Rate of Change formula on [a,b]	SLOPE
limit that represents the DEFINITION of the DERIVATIVE
Extreme Value Theorem (where could absolute extrema occur?)	f is continuous on [a,b] f will have an absolute max and min at either the endoints or at the critical points
Growth and Decay Formula "the rate at which population grows is proportional to the original amount (or amount present)"
Logistic Equation dP/dt =
Mean Value Theorem
given velocity, want to find s(a). You are given s(b).
How do you find displacement of a particle between time a and b.	Area under velocity curve gives displacement.
Speed increases: Speed decreases:	Speed increases: velocity and acceleration have same signs Speed decreases: velocity and acceleration have different signs
particle changes direction when	velocity changes sign
s(t) = position function s ' (t) = s " (t) =	s ' (t) = velocity s " (t) = acceleration
Total Distance Traveled
Particle moves: Left/down when __________ Right/up when __________	(left/down) velocity < 0 (right/up) velocity > 0
Particle is stopped when	v(t) = 0