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let me help you Ace your Calculus one final exam Im going to work through many many problems the first set of which are true false questions that are tricky theoretical ones but I will quickly move on to many calculations and applications number one true or false if F Prime of X is always positive for all X in some interval therefore Id also be assuming implicitly that f is differentiable on that interval the conclusion is then f is increasing on that interval this is true its a theorem its called the increasing function theorem you can look it up its based on the mean value theorem which will also come up in these questions you can prove it with that certainly sounds true if the slope of tangent lines are always positive the function should be going up number two this is tricky if f is differentiable and increasing on the interval then F Prime of X is always positive for all X in that interval that is actually false it sounds true the function is dif
