Let f ( x ) := x 2 − x + 5 x 2 + 3 {\displaystyle {}f(x):={\frac {x^{2}-x+5}{x^{2}+3}}} . Determine a polynomial h {\displaystyle {}h} of degree ≤ 3 {\displaystyle {}\leq 3} , with the property that its linear approximation at the points x = 0 {\displaystyle {}x=0} and x = 1 {\displaystyle {}x=1} coincide with those of f {\displaystyle {}f} .
