Rules and theorems
The product rule
What is f'g+g'f?
The derivative of this function is always zero
What is a constant?
This occurs whenever f'(x) = 0.
What is a critical point (maximum or minimum)?
This word is used to describe an integral with lower and upper limits (a and b).
What is "definite"?
This mathematician co-invented calculus and also formulated laws of motion.
Who is Isaac Newton?
The rule used to differentiate functions such as sin(x2).
What is the chain rule?
The derivative of this function is itself
What is ex?
This is the geometric interpretation of the derivative.
What is the slope of the tangent line?
This occurs when integrating a function below the x-axis.
What is negative area?
This mathematician's name is often mentioned when approximating area under a curve using rectangles.
Who is Bernhard Riemann? Or, what are Riemann Sums?
The quotient rule
What is (f'g-g'f)/g2?
This function has derivative -cos(x).
What is sin(x)?
A function has this feature wherever f''(x)=0.
What is an inflection point?
This antiderivative is equivalent to ∫3x2dx.
What is x3+c?
Despite being taught after derivatives, this concept was discovered first due to its application to area problems
What is integration?
This technique is used to find dy/dx given the equation 5xy-y3=8.
What is implicit differentiation?
The derivative of this function is 1/x.
What is natural log (ln)?
A graph has this feature if its derivative is increasing
What is concave up?
A student uses the formula
∫(top-bottom)dx
to find this.
What is area between curves?
This German mathematican invented the integral sign and dy/dx notation.
Who is Gottfried Wilhelm Leibniz?
This theorem connects integration to differentiation and lets us compute definite integrals by finding F(b)-F(a).
What is the fundamental theorem of calculus?
This function does not have a derivative at x=0 due to a "cusp" or sharp corner.
What is the absolute value function (|x|)?
A function displays this behavior if f'(x)>0 and f''(x)<0.
What is increasing and concave down?
If a function is increasing, this happens when estimating area using left-endpoint rectangles
What is an underestimate?
This paradox created by the Greek philosopher Zeno was difficult to resolve before calculus. It involves racing against -- but never being able to catch up to -- a slower opponent.
What is Achilles and the tortoise?