1.1. The figure below shows the curve with equation $y=f(x)$ where

$f(x)=2{x}^{2}-2{x}^{3}+3$

• The equation $f(x)=0$ has only one solution, $x= \alpha$

• You may assume that $f(x)$ is continuous for all values of $x$

(i) Find $f(1.5)$

(ii) Find$f(1.6)$

1.2. Use part (a) to write down an interval containing the root $\alpha$, in the form

a< \alpha </p><p style="line-height: 1.7" class="text-lg tracking-wide font-normal leading-relaxed">where \(a and $b$ are constants to be found.