Calculus Relationship Status
Why did the function break up with the tangent line?
Because it felt like they only touched once and then went in completely different directions.
You set your car’s cruise control to exactly 65 mph and drive down a straight highway for an hour. What is your acceleration during that hour?
Zero!
Since your velocity is constant, its derivative (acceleration) is zero.
I am a point on a graph. To my left, the graph is a happy bowl holding water. To my right, the graph is a sad umbrella shedding water. What kind of point am I?
An Inflection Point (where concavity changes!).
Which two famous 17th-century mathematicians famously threw absolute shade at each other for decades over who actually invented Calculus first?
Isaac Newton and Gottfried Wilhelm Leibniz.
Why are calculus teachers the absolute best at planning parties?
Because they know exactly how to maximize the fun while staying within the given boundaries (Optimization!)
Or anything close!!!
If a particle’s velocity is negative, but its acceleration is also negative, is the particle speeding up or slowing down?
Speeding up! (Since the signs match)
If you apply the Chain Rule to a Russian nesting doll, which doll do you differentiate first?
The outermost doll (leaving the inner dolls completely untouched), then work your way in!
Which rule did we use this year that shares a name with an upscale hotel, a cracker, or a fancy French guy who didn't actually invent the rule himself?
L'Hôpital's Rule
(Bonus points if you spelled it correctly!).
What do you call a student who actually remembers to write +C on an indefinite integral?
An integral part of the class.
Translate this calculus sentence into a relatable human emotion: "My happiness function has a first derivative greater than zero, but a second derivative less than zero."
"I am getting happier, but my burnout is starting to kick in." (Increasing at a decreasing rate).
What does a vertical asymptote say to a curve that tries to get too close?
you can't touch this!
What was the single most common phrase, warning, or mistake heard in this classroom over the last 5 days of review?
There are various acceptable answers to this!
Why was the calculus book so incredibly depressed after the final exam?
Because it had way too many problems.
What is the real-world difference between finding the integral of velocity (displacement) vs. the integral of speed (total distance) when running a marathon?
Displacement tells you how far you ended up from the starting line (0 if it's a loop!). Total distance tells you how much your feet actually hurt.
If f'(x) crosses the x-axis from above the axis to below the axis, what just happened to the original graph of f(x)?
It reached a Local Maximum.
What major global event forced a young Isaac Newton to stay at home on a farm, where he casually invented Calculus out of sheer boredom?
The Great Plague of London (1665). In 1665, the University of Cambridge shut down due to the Great Plague of London. A 22-year-old student named Isaac Newton had to sent home to his family's farm for a two-year "remote learning" quarantine. With literally nothing else to do, he casually invented Calculus, discovered the laws of optics, and figured out gravity.