AP Calculus BC Exam, AP Calculus BC

AP CALCULUS BC EXAM, AP CALCULUS BC
CORRECT ANSWERS UPDATED VERSION



Intermediate Value Theorem - CORRECT ANSWER -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.


Average Rate of Change - CORRECT ANSWER -Slope of secant line
between two points, use to estimate instantanous rate of change at a
point.


Instantenous Rate of Change - CORRECT ANSWER -Slope of tangent
line at a point, value of derivative at a point


Formal definition of derivative - CORRECT ANSWER -


Alternate definition of derivative - CORRECT ANSWER -limit as x
approaches a of [f(x)-f(a)]/(x-a)


When f '(x) is positive, f(x) is - CORRECT ANSWER -increasing


When f '(x) is negative, f(x) is - CORRECT ANSWER -decreasing


When f '(x) changes from negative to positive, f(x) has a - CORRECT
ANSWER -relative minimum


When f '(x) changes from positive to negative, f(x) has a - CORRECT
ANSWER -relative maximum

, When f '(x) is increasing, f(x) is - CORRECT ANSWER -concave up


When f '(x) is decreasing, f(x) is - CORRECT ANSWER -concave down


When f '(x) changes from increasing to decreasing or decreasing to
increasing, f(x) has a - CORRECT ANSWER -point of inflection


When is a function not differentiable - CORRECT ANSWER -corner,
cusp, vertical tangent, discontinuity


Product Rule - CORRECT ANSWER -uv' + vu'


Quotient Rule - CORRECT ANSWER -(uv'-vu')/v²


Chain Rule - CORRECT ANSWER -f '(g(x)) g'(x)


y = x cos(x), state rule used to find derivative - CORRECT ANSWER -
product rule


y = ln(x)/x², state rule used to find derivative - CORRECT ANSWER -
quotient rule


y = cos²(3x) - CORRECT ANSWER -chain rule


Particle is moving to the right/up - CORRECT ANSWER -velocity is
positive