u/socratictutoring

If you haven't seen EVT/IVT/MVT, you can skip this one!

Hint 1: >!proof by contradiction. Assume there are three zeros.!<

Hint 2: >!Apply Rolle's theorem twice. !<

Easier unit 4 problem - so go for it even if you've only just seen the derivative :)

Edit: my bad - this is a case where a "for all" would have been useful, the true or false is a bit confusing. Indeed, it depends on the function f. Knowing the derivative is positive at 2 gives us no information about the value of the function in a larger neighborhood of 2.

Hint: >!We don't know if f'(0) exists, so product rule can't be applied! Need to go back to the definition of the derivative.!<

Another limits one, but in a very different direction :)

Skipping the tricks today (they'll be back!). See if you can do this one in under 90 seconds :)

Note: Can't edit image, but ignore option IV - indicate which are true, can be more than one :)

Last problem with limit trickiness unless I get requests!
Worthwhile to compare this one with challenge 7. Hint:>!Specifically, consider the differences when you're deciding if III is true. !<

Hint: >!write out the limit definition of the derivative at x = 2, using lim x->2 format instead of h -> 0 format. !<

Additional step: confirm this solution is valid by considering the limit where air resistance is 0!

This one might be a bit of a challenge - I've noticed that many AP Physics C courses tend to skip drag, as not all students have seen differential equations yet.

If your course skipped this, let me know in the comments!

Additional Challenge: what if this took place in an elevator, accelerating upwards with acceleration a?