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AP Calc BC_ Formulas (Final) Exam with complete solutions 2024_2025.
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AP Calc BC_ Formulas (Final) Exam with complete solutions 2024_2025.
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AP Calc BC: Formulas (Final) Exam withcomplete solutions 2024/2025
Intermediate Value Theorem - 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 - ANSWER-Slope of secant line between two points, use
to estimate instantanous rate of change at a point.
Instantenous Rate of Change - ANSWER-Slope of tangent line at a point, value of
derivative at a point
Formal definition of derivative - ANSWER-limit as h approaches 0 of [f(a+h)-f(a)]/h
Alternate definition of derivative - ANSWER-limit as x approaches a of
[f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - ANSWER-increasing
When f '(x) is negative, f(x) is - ANSWER-decreasing
When f '(x) changes from negative to positive, f(x) has a - ANSWER-relative
minimum
When f '(x) changes fro positive to negative, f(x) has a - ANSWER-relative
maximum
When f '(x) is increasing, f(x) is - ANSWER-concave up
When f '(x) is decreasing, f(x) is - ANSWER-concave down
, When f '(x) changes from increasing to decreasing or decreasing to increasing,
f(x) has a - ANSWER-point of inflection
When is a function not differentiable - ANSWER-corner, cusp, vertical tangent,
discontinuity
Product Rule - ANSWER-uv' + vu'
Quotient Rule - ANSWER-(uv'-vu')/v²
Chain Rule - ANSWER-f '(g(x)) g'(x)
y = x cos(x), state rule used to find derivative - ANSWER-product rule
y = ln(x)/x², state rule used to find derivative - ANSWER-quotient rule
y = cos²(3x) - ANSWER-chain rule
Particle is moving to the right/up - ANSWER-velocity is positive
Particle is moving to the left/down - ANSWER-velocity is negative
absolute value of velocity - ANSWER-speed
y = sin(x), y' = - ANSWER-y' = cos(x)
y = cos(x), y' = - ANSWER-y' = -sin(x)
y = tan(x), y' = - ANSWER-y' = sec²(x)
y = csc(x), y' = - ANSWER-y' = -csc(x)cot(x)
y = sec(x), y' = - ANSWER-y' = sec(x)tan(x)
y = cot(x), y' = - ANSWER-y' = -csc²(x)
y = sin⁻¹(x), y' = - ANSWER-y' = 1/√(1 - x²)
y = cos⁻¹(x), y' = - ANSWER-y' = -1/√(1 - x²)
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