Numerical Derivatives using Polynomial Representation. An anemometer measures

the wind speed. During calibration the the output signal, $E,$ is measured as $0,1\mathrm{.}7,3\mathrm{.}3,$ and

$5\mathrm{.}6$ at velocities, $V,0,1,1\mathrm{.}5$ and $2\frac{m}{s}$ respectively.

$($a$)$ Use a single polynomial expression to represent $E(V).$ Compute all constants in the

expression.

$($b$)$ Obtain the gradient $d\frac{E}{d}V$ at $v=1$