The Squeeze Theorem - UCLA Mathematics
h!0 (x+ h) x3 h = lim h!0 x3 + 3hx2 + 3h2x+ h3 3x3 h = lim h!0 3hx2 + 3h2x+ h h = lim h!0 (3x 2+ 3hx+ h2) = 3x; whenever this limit exists. But this limit exists for all x-values, so fis everywhere di eren-tiable, and f0(x) = 3x2 for all xvalues. One thing we notice immediately is that constant functions have derivative 0. To see this, notice ... ................
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