AP Calculus BC questions 100%
CORRECT!!
Squeeze Theorem - ANSWERIf h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval
containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim
x→c ƒ(x) exists and equals L.
Continuity - ANSWERA function ƒ is continuous at c if:
a. ƒ(c) is defined
b. lim x→c ƒ(x) exists
c. lim x→c ƒ(x) = ƒ(c)
Intermediate Value Theorem - ANSWERIf ƒ is continuous on an interval [a,b] and k
is any number between ƒ(a) and ƒ(b), there is at least one number c in [a,b] such
that ƒ(c) = k.
Definition of the derivative - ANSWERƒ'(x) = lim h→0 (ƒ(x+h) - ƒ(x))/h
Power rule - ANSWERd/dx xⁿ = nx^(n-1)
Product rule - ANSWERd/dx ƒ(x)g(x) = ƒ'(x)g(x) + ƒ(x)g'(x)
Quotient rule - ANSWERd/dx ƒ(x)/g(x) = (g(x)ƒ'(x) - ƒ(x)g'(x))/g²(x)
Chain rule - ANSWERd/dx ƒ(g(x)) = ƒ'(g(x))g'(x)
Implicit differentiation - ANSWERd/dx ƒ(y) = ƒ'(y)(dy/dx)
Definition of a minimum - ANSWERƒ(c) is the minimum of ƒ on an interval if ƒ(c) ≤
f(x) for all x contained in the interval.
Definition of a maximum - ANSWERƒ(c) is the maximum of ƒ on an interval if ƒ(c) ≥
f(x) for all x contained in the interval.
Extreme Value Theorem - ANSWERIf ƒ is continuous on a closed interval, then ƒ
has both a minimum and maximum on the interval.
Critical number - ANSWERA number c is called critical if ƒ'(c) = 0 or ƒ is not
differentiable at c.
Points tested for minima/maxima - ANSWERCritical points and enpoints.
Local minimum/maximum - ANSWERA point where ƒ' changes from positive to
negative or vice versa.
Inflection point - ANSWERA point where ƒ" changes from positive to negative or vice
versa.
CORRECT!!
Squeeze Theorem - ANSWERIf h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval
containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim
x→c ƒ(x) exists and equals L.
Continuity - ANSWERA function ƒ is continuous at c if:
a. ƒ(c) is defined
b. lim x→c ƒ(x) exists
c. lim x→c ƒ(x) = ƒ(c)
Intermediate Value Theorem - ANSWERIf ƒ is continuous on an interval [a,b] and k
is any number between ƒ(a) and ƒ(b), there is at least one number c in [a,b] such
that ƒ(c) = k.
Definition of the derivative - ANSWERƒ'(x) = lim h→0 (ƒ(x+h) - ƒ(x))/h
Power rule - ANSWERd/dx xⁿ = nx^(n-1)
Product rule - ANSWERd/dx ƒ(x)g(x) = ƒ'(x)g(x) + ƒ(x)g'(x)
Quotient rule - ANSWERd/dx ƒ(x)/g(x) = (g(x)ƒ'(x) - ƒ(x)g'(x))/g²(x)
Chain rule - ANSWERd/dx ƒ(g(x)) = ƒ'(g(x))g'(x)
Implicit differentiation - ANSWERd/dx ƒ(y) = ƒ'(y)(dy/dx)
Definition of a minimum - ANSWERƒ(c) is the minimum of ƒ on an interval if ƒ(c) ≤
f(x) for all x contained in the interval.
Definition of a maximum - ANSWERƒ(c) is the maximum of ƒ on an interval if ƒ(c) ≥
f(x) for all x contained in the interval.
Extreme Value Theorem - ANSWERIf ƒ is continuous on a closed interval, then ƒ
has both a minimum and maximum on the interval.
Critical number - ANSWERA number c is called critical if ƒ'(c) = 0 or ƒ is not
differentiable at c.
Points tested for minima/maxima - ANSWERCritical points and enpoints.
Local minimum/maximum - ANSWERA point where ƒ' changes from positive to
negative or vice versa.
Inflection point - ANSWERA point where ƒ" changes from positive to negative or vice
versa.
