Test 1: Calculus
Instruction: Create a pdf file with all the solutions, upload file on Google Drive and share the link in the form shared at the bottom of the page
1) If $f(x)$ is derivable in the interval $[a-h, a+h]$, prove that
(i) f(a+h)−f(a−h)=h[f′(a+θ1h)+f′(a−θ1h)], where 0<θ1<1
(ii) f(a+h)−2f(a)+f(a−h)=h[f′(a+θ2h)−f′(a−θ2h)], where 0<θ2<1