如果函数y=f(x)在x=0处得导数存在,且f(x)=f(-x)求f‘(0)的值
问题描述:
如果函数y=f(x)在x=0处得导数存在,且f(x)=f(-x)求f‘(0)的值
答
f(x) = f(-x)f'(0-)= lim(y->0-) { [f(y) - f(0)]/y } = lim(y->0-) { [f(-y) - f(0)] / (y) }= -lim(y-> 0-) { [f(-y) - f(0)]/ (-y) }= -lim(-y-> 0+){ [f(-y) - f(0)]/ (-y) } = - f'(0+)f'(0) => f'(0+) = f'(0-...