176. Given the functions $f(x)=x^{2}-x$ and $g(x)=x^{2}+x$. It is required to determine: a) at what value of the argument the function $f(x)$ increases twice as fast as $g(x) ; \sigma)$ does there exist a value of $x$ at which the functions change at the same rate?
Solution. a) We find the derivatives of the given functions: $f^{\prime}(x)=$ $=2 x-1$ and $g^{\prime}(x)=2 x+1$ (see solutions of examples 172 and 173). According to the condition, the equality $2 x-1=2(2 x+1)$ must hold; solving this equation, we find $x=-3 / 2$.

b) Since the equation $2 x-1=2 x+1$ has no real roots, the answer to the given question is negative.