For the function $$$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$$

$$f(x)$$ is cubic polynomial with $$f(2)=18$$ and $$f(1)=-1$$. Also $$f(x)$$ has local maxima at $$x=-1$$ and $$f'(x)$$ has local minima at $$x=0$$, then

Let $$f\left( x \right) = \left\{ {\matrix{ {{e^x},} & {0 \le x \le 1} \cr {2 - {e^{x - 1}},} & {1 < x \le 2} \cr {x - e,} & {2 < x \le 3} \cr } } \right.$$ and $$g\left( x \right) = \int\limits_0^x {f\left( t \right)dt,x \in \left[ {1,3} \right]} $$
then $$g(x)$$ has

The function $$f\left( x \right) = \int\limits_{ - 1}^x {t\left( {{e^t} - 1} \right)\left( {t - 1} \right){{\left( {t - 2} \right)}^3}\,\,\,{{\left( {t - 3} \right)}^5}} $$ $$dt$$ has a local minimum at $$x=$$