AP Calculus BC Exam, AP Calculus BC
Questions and Answers
Intermediate Value Theorem - Correct Answers -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 Answers -Slope of secant line between two points,
use to estimate instantanous rate of change at a point.
Instantenous Rate of Change - Correct Answers -Slope of tangent line at a point, value
of derivative at a point
Formal definition of derivative - Correct Answers -
Alternate definition of derivative - Correct Answers -limit as x approaches a of
[f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - Correct Answers -increasing
When f '(x) is negative, f(x) is - Correct Answers -decreasing
When f '(x) changes from negative to positive, f(x) has a - Correct Answers -relative
minimum
When f '(x) changes from positive to negative, f(x) has a - Correct Answers -relative
maximum
When f '(x) is increasing, f(x) is - Correct Answers -concave up
When f '(x) is decreasing, f(x) is - Correct Answers -concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has
a - Correct Answers -point of inflection
When is a function not differentiable - Correct Answers -corner, cusp, vertical tangent,
discontinuity
Product Rule - Correct Answers -uv' + vu'
Quotient Rule - Correct Answers -(uv'-vu')/v²
Chain Rule - Correct Answers -f '(g(x)) g'(x)
Questions and Answers
Intermediate Value Theorem - Correct Answers -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 Answers -Slope of secant line between two points,
use to estimate instantanous rate of change at a point.
Instantenous Rate of Change - Correct Answers -Slope of tangent line at a point, value
of derivative at a point
Formal definition of derivative - Correct Answers -
Alternate definition of derivative - Correct Answers -limit as x approaches a of
[f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - Correct Answers -increasing
When f '(x) is negative, f(x) is - Correct Answers -decreasing
When f '(x) changes from negative to positive, f(x) has a - Correct Answers -relative
minimum
When f '(x) changes from positive to negative, f(x) has a - Correct Answers -relative
maximum
When f '(x) is increasing, f(x) is - Correct Answers -concave up
When f '(x) is decreasing, f(x) is - Correct Answers -concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has
a - Correct Answers -point of inflection
When is a function not differentiable - Correct Answers -corner, cusp, vertical tangent,
discontinuity
Product Rule - Correct Answers -uv' + vu'
Quotient Rule - Correct Answers -(uv'-vu')/v²
Chain Rule - Correct Answers -f '(g(x)) g'(x)
