若函数f(x)在点a可导,则lim (f(a-f(a+2h)))/3h = ( )h→0
A: 2f'(a)/3
B: -3f'(a)/2
C: -2f'(a)/3
D: 3f'(a)/2
A: 2f'(a)/3
B: -3f'(a)/2
C: -2f'(a)/3
D: 3f'(a)/2
举一反三
- 若函数$f(x)$在点$a$处具有连续的二阶导函数,则$$\lim_{h\to 0}\frac{f(a+h)+f(a-h)-2f(a)}{h^2}=f''(a)$$
- 已知\(f(x)\)在节点1,2处的函数值为\(f(1) = 2,f(2) = 3\) ,在节点1,2处的导数值为\(f'(1) = 0,f'(2) = - 1\) ,求 f(x) 两点三次埃米特插值多项式 A: \(H(x) = - 3{x^3} + 13{x^2} - 17x + 6\) B: \(H(x) = - 3{x^3} + 13{x^2} - 17x + 3\) C: \(H(x) = - 3{x^3} + 13{x^2} - 17x +7\) D: \(H(x) = - 3{x^3} + 13{x^2} - 17x + 9\)
- 已知\( y = {f^2}(x) \),假设\( f(u) \)二阶可导,则 \( y'' \)为( ). A: \( 2{[f'(x)]^2} + 2f(x)f'(x) \) B: \( 2[f'(x)] + 2f(x)f''(x) \) C: \( 2{[f'(x)]^2} + 2f(x)f''(x) \) D: \( 2{[f'(x)]^2} + f(x)f''(x) \)
- 随机变量X在区间(-1,2)上均匀分布,F(x)是X的分布函数,则以下结果正确的是 A: F(0.5)=0.5 B: F(1)=2/3 C: F(0)=0 D: F(-0.5)=0.5 E: F(1)=1/3 F: F(1.5)=3/4 G: F(2)=0 H: F(3)=0
- 设函数f(x)在x=1处可导,且lim h→0 f(1)-f(1+2h)/h=-1/2,则f'(1)=() A: -1/2 B: 1/2 C: 1/4 D: -1/4