<p>does anyone know the difference between proving a function is continuous and proving something is differentiable? are there any good sites that help with these topics?</p>

<p>Well it's continuous if f(x) exists at the point you're looking at.</p>

<p>It's differentiable if the derivitives are the same from the left and right at that point.</p>

<p>To prove continuity, you have to show that there are no discontinuities in that interval, such as: jump (usually in a piecewise function, in which case you just check that the endpoint values agree), removable (looks like a hole in the graph), and asymptote (usually in a rational function, in which case you check the denominator for zero).</p>

<p>To prove differentiability, you have to show that the left-hand and right-hand limits of the derivative expression both exist and are equal.</p>

<p>Shouldn't your textbook give you a clear explanation? At least my textbook does.</p>

<p>use the definiton of continuity to prove if a function is continuous. 1) f(a) must exist 2) lim x approaches a f(x) must exist 3) f(a) must equal lim x approaches f(x). to see if a function is differentiable use the definition. lim h approaches 0 f(x+h)-f(x)/h and see if there is a general form for every point</p>

<p>If a function is differentiable, it has to be continuous (but it's not true the other way around).

Continuous means that the function value at every point equals the limit at that point.

Differentiable means that the limit from both sides exist and are equal to each other.</p>