Answer
$$-7.28,\ \ 0.32,\ \ 4.39 \%$$
Work Step by Step
Given $$f(x)=2 x^{2}-x, \quad a=5, \quad \Delta x=-0.4$$ Since $$ f'(x) = 4x-1 ,\ \ \ f'(3)=19 $$ Then \begin{align*} \Delta f &\approx f^{\prime}(a) \Delta x\\ &=(19)(-0.4)\\ &= -7.6 \end{align*} Since the change $\Delta f$ is given by \begin{align*} \Delta f&=f(a+\Delta x)-f(a)\\ &=f(4.6)-f(5)\\ &=37.72-45\\ & \approx -7.28 \end{align*} to find error $$|-7.28+7.6|=0.32$$ and the percentage $$\frac{0.32}{7.28} \times 100 \% \approx 4.39 \%$$
