高数中值定理问题1、设f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导,且|f'(x)|≤M,f(0)=0,则必有A |f(x)|≥M B |f(x)|>M C f(x)|≤M D f(x)|<M2、若f(x)在开区间(a,b)内可导,且对(a,b)内任意两点x1、x2,恒有|
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![高数中值定理问题1、设f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导,且|f'(x)|≤M,f(0)=0,则必有A |f(x)|≥M B |f(x)|>M C f(x)|≤M D f(x)|<M2、若f(x)在开区间(a,b)内可导,且对(a,b)内任意两点x1、x2,恒有|](/uploads/image/z/5348064-48-4.jpg?t=%E9%AB%98%E6%95%B0%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E9%97%AE%E9%A2%981%E3%80%81%E8%AE%BEf%28x%29%E5%9C%A8%E9%97%AD%E5%8C%BA%E9%97%B4%5B-1%2C1%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%E5%BC%80%E5%8C%BA%E9%97%B4%28-1%2C1%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94%7Cf%27%28x%29%7C%E2%89%A4M%2Cf%280%29%3D0%2C%E5%88%99%E5%BF%85%E6%9C%89A+%7Cf%28x%29%7C%E2%89%A5M+B+%7Cf%28x%29%7C%EF%BC%9EM+C+f%28x%29%7C%E2%89%A4M+D+f%28x%29%7C%EF%BC%9CM2%E3%80%81%E8%8B%A5f%28x%29%E5%9C%A8%E5%BC%80%E5%8C%BA%E9%97%B4%28a%2Cb%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94%E5%AF%B9%28a%2Cb%29%E5%86%85%E4%BB%BB%E6%84%8F%E4%B8%A4%E7%82%B9x1%E3%80%81x2%2C%E6%81%92%E6%9C%89%7C)
高数中值定理问题1、设f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导,且|f'(x)|≤M,f(0)=0,则必有A |f(x)|≥M B |f(x)|>M C f(x)|≤M D f(x)|<M2、若f(x)在开区间(a,b)内可导,且对(a,b)内任意两点x1、x2,恒有|
高数中值定理问题
1、设f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导,且|f'(x)|≤M,f(0)=0,则必有
A |f(x)|≥M B |f(x)|>M C f(x)|≤M D f(x)|<M
2、若f(x)在开区间(a,b)内可导,且对(a,b)内任意两点x1、x2,恒有|f(x2)-f(x1)|≤(x2-x1)^2,则必有
A f'(x)≠0 B f'(x)=x C f(x)=x D f(x)=C(常数)
高数中值定理问题1、设f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导,且|f'(x)|≤M,f(0)=0,则必有A |f(x)|≥M B |f(x)|>M C f(x)|≤M D f(x)|<M2、若f(x)在开区间(a,b)内可导,且对(a,b)内任意两点x1、x2,恒有|
因为f(x)在闭区间[-1,1]上连续,在开区间(-1,1)内可导
所以|f(x)|=|f(x)-f(0)|=|∫f'(x)dx|<=∫|f(x)|dx<=M*1=M
选C
设x2=x1+Δx(Δx≠0)
则|f(x2)-f(x1)|/|x2-x1|<=|x2-x1|
即|f(x1+Δx)-f(x1)|/|Δx|<=|Δx|
两边取极限Δx->0
则|f'(x1)|<=0
所以f'(x1)=0
所以f(x)=C
选D
第一题选则D,第二题选择C