作业帮设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明:至少存在一点C∈(0,a),使得f(C)+Cf '(C)=0后面是3f(C)+Cf '(C)=0
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![设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明:至少存在一点C∈(0,a),使得f(C)+Cf '(C)=0后面是3f(C)+Cf '(C)=0](/uploads/image/z/6974052-60-2.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5B0%2Ca%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%280%2Ca%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%28a%29%3D0%2C%E8%AF%81%E6%98%8E%3A%E8%87%B3%E5%B0%91%E5%AD%98%E5%9C%A8%E4%B8%80%E7%82%B9C%E2%88%88%280%2Ca%29%2C%E4%BD%BF%E5%BE%97f%28C%29%2BCf+%27%28C%29%3D0%E5%90%8E%E9%9D%A2%E6%98%AF3f%28C%29%2BCf+%27%28C%29%3D0)
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设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明:至少存在一点C∈(0,a),使得f(C)+Cf '(C)=0后面是3f(C)+Cf '(C)=0
设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明:至少存在一点C∈(0,a),使得f(C)+Cf '(C)=0
后面是3f(C)+Cf '(C)=0
设f(x)在[0,a]上连续,在(0,a)内可导,且f(a)=0,证明:至少存在一点C∈(0,a),使得f(C)+Cf '(C)=0后面是3f(C)+Cf '(C)=0
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则 g(0)=g(a) = 0,根据中值定理,存在 C,0
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