AP Calculus BC Exam, AP Calculus BC Questions and Correct Answers/ Latest Update / Already Graded

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AP Calculus BC Exam, AP Calculus BC
Questions and Correct Answers/ Latest
Update / Already Graded
Intermediate Value Theorem

Ans: 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

Ans: Slope of secant line between two points, use to estimate
instantanous rate of change at a point.


Instantenous Rate of Change

Ans: Slope of tangent line at a point, value of derivative at a
point


Formal definition of derivative

Ans:


Alternate definition of derivative

Ans: limit as x approaches a of [f(x)-f(a)]/(x-a)


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When f '(x) is positive, f(x) is

Ans: increasing


When f '(x) is negative, f(x) is

Ans: decreasing


When f '(x) changes from negative to positive, f(x) has a

Ans: relative minimum


When f '(x) changes from positive to negative, f(x) has a

Ans: relative maximum


When f '(x) is increasing, f(x) is

Ans: concave up


When f '(x) is decreasing, f(x) is

Ans: concave down




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When f '(x) changes from increasing to decreasing or decreasing to
increasing, f(x) has a

Ans: point of inflection


When is a function not differentiable

Ans: corner, cusp, vertical tangent, discontinuity


Product Rule

Ans: uv' + vu'


Quotient Rule

Ans: (uv'-vu')/v²


Chain Rule

Ans: f '(g(x)) g'(x)


y = x cos(x), state rule used to find derivative

Ans: product rule


y = ln(x)/x², state rule used to find derivative

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