Re: HSC 2013 4U Marathon
Some random calculus true/false practice for multiple choice:
1. Every continuous function is differentiable.
2. Every differentiable function is continuous.
3. Every differentiable function has a continuous derivative.
4. If a differentiable f attains a maximum at some c in the interval a <= c <= b, then f'(a)=0.
5. Which of these is a stronger statement: f is differentiable on the interval (a,b) vs f has an definite integral over the interval (a,b).
6. If a function f defined on R has a maximum at a, then f''(a) > 0.
7. If a < b, f(a) < 0, and f(b) > 0, then f(c)=0 for some c between a and b.
8. If f is differentiable at a and f'(a) is nonzero, then f has a differentiable inverse function near a.
Some justification would be nice unless you think it is obvious.