Uhh few simple questions..

under what circumstance is function of f(x) differentiate-able, is it the vertical tangent line or horizontal tangent line that make it unable to differentiate? Also what is defined as in discontinuities in the graph to make it undifferentiatable?

how can we determine whether to use mean value theorem or average value theorem under specific function?

which approximations method can get you the least estimated error? left riemann sum, right riemann sum, or trapezoidal rule?

anyone in calculus that can help me out? my BC finals is tomorrow =(