AP Calculus AB Derivatives — practice questions
44 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP Calculus AB Derivatives in the app →A student differentiates f(x) = x^5 using the power rule. The derivative is:A cost function is the constant f(x) = 7. Its derivative is:For f(x) = 3x^2, a student pulls the 3 out and differentiates the rest. The derivative is:If f(x) = x^3 + x, then f'(x) equals:A function is written as one function multiplied by another. The rule to reach for is the:A student guesses the derivative of a product is simply the product of the derivatives. Is that right?A function appears as one function divided by another. The rule to use is the:A student meets a composition, with one function sitting inside another. The rule for that is the:Differentiating f(x) = (2x + 1)^3 with the chain rule gives:A physics student needs the derivative of sin x. It is:The same student now needs the derivative of cos x. It is:A function is known to be differentiable at a point. What follows about continuity there?Another function is continuous at a point. Must it also be differentiable there?A student differentiates the derivative one more time. The result is the:Third and fourth derivatives, and those beyond, are known together as:Velocity is the rate of change of position. The rate of change of velocity is:An equation cannot be solved neatly for y, so a student differentiates both sides as they stand. That method iKnowing the derivative of a function, a student can also compute the derivative of its:A student differentiates e^x. The result is:The inverse of the natural exponential function has its own name. It is the:A calculus course opens by going back to secant lines and one other kind of line. That other kind is:Average speed over a whole trip differs from speed at one instant. That second quantity is: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