Mastering Free-Response Questions in AP Calculus AB

What is the product rule used for in calculus?

• To find limits of functions

• To integrate functions

• To differentiate products of functions

• To differentiate sums of functions

If f(x) = g(x) * h(x), what is f'(x) according to the product rule?

• g'(x) * h'(x)

• g(x) * h'(x) + h(x) * g'(x)

• g(x) / h(x) + h(x) / g(x)

• g(x) - h(x)

What is the derivative of the function P(x) = a(x) * b(x) at x = -3?

• a(-3) / b(-3) + b(-3) / a(-3)

• a(-3) * b'(-3) + b(-3) * a'(-3)

• a(-3) + b(-3)

• a'(-3) * b'(-3)

What does the chain rule help to differentiate?

• Quotients of functions

• Products of functions

• Sums of functions

• Compositions of functions

How is the chain rule applied to the function C(x) = 5 * e^(a(x))?

• 5 * a'(x) * e^(a(x))

• 5 + e^(a(x))

• 5 * a(x) * e'(a(x))

• 5 / e^(a(x))

What is the derivative of an inverse function v(x) = a^(-1)(x) at x = -2?

• 1 / a'(-2)

• -1 / a'(-2)

• a'(-2)

• -a'(-2)

What is the reciprocal of the derivative of a function at a given point used for?

• To integrate the function

• To determine the slope of the tangent at that point

• To find the maximum value of the function

• To calculate the derivative of its inverse function at that point

What is the limit as x approaches 1 of a function that results in an indeterminate form 0/0?

• Undefined

• 0

• Can be found using L'Hopital's rule

• Infinity

What does L'Hopital's rule state about limits?

• It applies to limits resulting in the form 0 * infinity

• It only applies to polynomial functions

• It is used when limits result in the form 0/0 or infinity/infinity

• It simplifies limits by factoring

What is the result of applying L'Hopital's rule to the limit as x approaches 1 of a complicated quotient?

• 5/2

• 0

• Undefined

• 1