f(x)在[0,+∞)有连续导数,f'(x)>=k>0,f(0)
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f(x)在[0,+∞)有连续导数,f''(x)>=k>0,f(0)f(x)在[0,+∞)有连续导数,f''(x)>=k>0,f(0)f(x)在[0,+∞)有连续导数,f''(x)>=k>0,f(0)证明:(
f(x)在[0,+∞)有连续导数,f'(x)>=k>0,f(0)
f(x)在[0,+∞)有连续导数,f'(x)>=k>0,f(0)
f(x)在[0,+∞)有连续导数,f'(x)>=k>0,f(0)
证明:(\int_a^b 表示积分号,上限为b,下限为a,\inf表示无穷号)存在性:令a = -f(0)/k则有f(a) - f(0) = \int_0^a f'(x) dx >= \int_0^a k dx = ka即f(a) >= ka + f(0) = -f(0) + f(0) = 0
即在[0,a]区间内 f(x)连续,且f(0)
f(x)在[0,+∞)有连续导数,f''(x)>=k>0,f(0)
f(x)在[0,+∞)有连续导数,f'(x)>=k>0,f(0)
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