UserAdmin

已知函数\[ f(x)=e^x-ax和g(x)=ax- \ln x \]有相同的最小值。

(1)求a;

(2)证明：存在直线y=b,其余两条曲线y=f(x)和y=g(x)共有三个不同的交点，且从左到右的三个交点的横坐标成等差数列。

The derivative of \({\sin \left( \frac{1}{x^2+1} \right)}\) is

\[ \frac{\mathrm{d}}{\mathrm{d}x} \sin \left( \frac{1}{x^2+1} \right) = {-\frac{2\cdot x\cdot \cos \left( \frac{1}{x^2+1} \right)}{{\left(x^2+1\right)}^2}} \]

You can input this as <code>-((2*x*cos(1/(x^2+1)))/(x^2+1)^2)</code>