AP Calculus BC Unit 2 Exam Questions
and Answers
derivative at a point - Correct Answers -using limits:
- lim [(f(x) - f(c)]/[x-c]
x->c
equation of tangent line:
1. find the derivative at a point
2. plug in points in point slope form (derivative is the slope)
normal line: perpendicular to tangent line
- negative reciprocal slope of tangent line's slope
power rule - Correct Answers -f(x) = x^n
f'(x) = nx^n-1
*has to be a VARIABLE raised to a REAL NUMBER (if it is a variable raised to a
variable then add ln on both sides to evaluate the derivative after)
product and quotient rule - Correct Answers -product rule: h(x) = f(x)g(x)
- h'(x) = f'(x)g(x) + g'(x)f(x)
quotient rule: h(x) = [f(x)/g(x)]
- h'(x) = [f'(x)g(x) - g'(x)f(x)]/[g(x)]^2
*sometimes the function can be combines or simplified to then find the derivative (log
rules or trig identities)
polar derivatives - Correct Answers -1. with the given r equation make the x equation
and y equation
- x = rcos(ϑ) & y = rsin(ϑ)
2. find the derivative of each respective equation
3. find dy/dx by dividng the derivative of the y equation by the derivative of the x
equation
*when finding a derivative at a theta value notation is always dy/dx | ϑ =__= derivative
value
vector derivatives - Correct Answers -any parametric equation can be turned into a
vector equation (ex. r(t) = < rcosϑ, rsinϑ >
- the first derivative of the vector equation represents the direction of tangent line
(sometimes velocity and when dy/dx = 0/0, the particle is at rest)
- second derivative can sometimes be acceleration
*if asked to find speed, it must be the positive magnitude value of velocity
chain rule - Correct Answers -h(x) = g(f(x))
h'(x) = g'(f(x))f'(x)
and Answers
derivative at a point - Correct Answers -using limits:
- lim [(f(x) - f(c)]/[x-c]
x->c
equation of tangent line:
1. find the derivative at a point
2. plug in points in point slope form (derivative is the slope)
normal line: perpendicular to tangent line
- negative reciprocal slope of tangent line's slope
power rule - Correct Answers -f(x) = x^n
f'(x) = nx^n-1
*has to be a VARIABLE raised to a REAL NUMBER (if it is a variable raised to a
variable then add ln on both sides to evaluate the derivative after)
product and quotient rule - Correct Answers -product rule: h(x) = f(x)g(x)
- h'(x) = f'(x)g(x) + g'(x)f(x)
quotient rule: h(x) = [f(x)/g(x)]
- h'(x) = [f'(x)g(x) - g'(x)f(x)]/[g(x)]^2
*sometimes the function can be combines or simplified to then find the derivative (log
rules or trig identities)
polar derivatives - Correct Answers -1. with the given r equation make the x equation
and y equation
- x = rcos(ϑ) & y = rsin(ϑ)
2. find the derivative of each respective equation
3. find dy/dx by dividng the derivative of the y equation by the derivative of the x
equation
*when finding a derivative at a theta value notation is always dy/dx | ϑ =__= derivative
value
vector derivatives - Correct Answers -any parametric equation can be turned into a
vector equation (ex. r(t) = < rcosϑ, rsinϑ >
- the first derivative of the vector equation represents the direction of tangent line
(sometimes velocity and when dy/dx = 0/0, the particle is at rest)
- second derivative can sometimes be acceleration
*if asked to find speed, it must be the positive magnitude value of velocity
chain rule - Correct Answers -h(x) = g(f(x))
h'(x) = g'(f(x))f'(x)
