AP Calculus BC Applications of Derivatives — practice questions
22 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP Calculus BC Applications of Derivatives in the app →Air is pumped into a balloon and both its radius and volume grow together. Linking the two rates of change is A student replaces a curve near one point with its tangent line to estimate values nearby. That estimate is thA point where the derivative is zero or undefined is called a:If a function has a local extremum at a point, that point must be a:The converse fails: a function with a critical point is not guaranteed to have there a:One theorem guarantees a continuous function on a closed, bounded interval attains both a highest and a lowestA special case of the Mean Value Theorem, applying when the endpoints have equal function values, is:To classify a critical point by looking at how the derivative's sign changes across it, a student uses the:A function is defined to be concave up on an interval when its derivative is:By the same logic a twice-differentiable function is concave down when its derivative is:Checking concavity through the sign of the second derivative is known as the:A point where the graph switches from concave up to concave down is a point of:Using the sign of the second derivative at a critical point to classify it is the:A farmer wants the largest area from a fixed length of fencing. Setting up and solving that kind of problem isA limit produces the form zero over zero, so its behaviour cannot be read off directly. That form is called:The rule that resolves such a limit by differentiating numerator and denominator separately is:An iterative technique for finding zeroes, built on tangent line approximations, is:Calculators and computers rely on that same tangent-based idea when they find:A function whose derivative is the given function is called its:Knowing an object's velocity, a student recovers its position by finding an:The notation used for a family of antiderivatives, complete with its constant, is the:A tank is draining and a student is asked how fast the depth falls when the volume is changing at a known rate