Ap Calculus Bc Comprehensive Assessment Questions And Solutions Graded A+

AP CALCULUS BC COMPREHENSIVE
ASSESSMENT QUESTIONS AND SOLUTIONS
GRADED A+

●● 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:


●● Alternate definition of derivative
Answer: limit as x approaches a of [f(x)-f(a)]/(x-a)


●● When f '(x) changes from negative to positive, f(x) has a
Answer: relative minimum


●● When f '(x) changes from positive to negative, f(x) has a
Answer: relative maximum

,●● When f''(x) is positive, f(x) is
Answer: concave up


●● When f ''(x) is negative, 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


●● absolute value of velocity
Answer: speed


●● 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 = tan⁻¹(x), y' =
Answer: y' = 1/(1 + x²)


●● y=y = sec⁻¹(x), y' =
Answer: y' = 1/|x|√(1 - x²)


●● y = a^x, y' =
Answer: y' = a^x ln(a)


●● y = ln(x), y' =
Answer: y' = 1/x


●● y = log (base a) x, y' =
Answer: y' = 1/(x lna)