function checkAnswer(){
  if (!(
     !(document.form1.x1a.checked) && 
     !(document.form1.x1b.checked) &&
     (document.form1.x1c.checked) &&
     (document.form1.x1d.checked) &&
     !(document.form1.x1e.checked) &&
     (document.form1.x1f.checked) &&
     !(document.form1.x1g.checked) 
     )){alert("Your answer for inflection points is incorrect.")}
  else 
  if (!(
     (document.form1.x2a.checked) && 
     (document.form1.x2b.checked) &&
     (document.form1.x2c.checked) &&
     (document.form1.x2d.checked) &&
     (document.form1.x2e.checked) &&
     (document.form1.x2f.checked) &&
     (document.form1.x2g.checked) 
     )){alert("Your answer for f '(x)>0 is incorrect.")}
  else 
  if (!(
     !(document.form1.x3a.checked) && 
     !(document.form1.x3b.checked) &&
     !(document.form1.x3c.checked) &&
     !(document.form1.x3d.checked) &&
     !(document.form1.x3e.checked) &&
     !(document.form1.x3f.checked) &&
     !(document.form1.x3g.checked) 
     )){alert("Your answer for local maxima is incorrect.")}
  else 
  if (!(
     (document.form1.x4a.checked) && 
     (document.form1.x4b.checked) &&
     !(document.form1.x4c.checked) &&
     !(document.form1.x4d.checked) &&
     (document.form1.x4e.checked) &&
     !(document.form1.x4f.checked) &&
     !(document.form1.x4g.checked) 
     )){alert("Your answer for concave up is incorrect.")}
  else 
  if (!(
     !(document.form1.x5a.checked) && 
     !(document.form1.x5b.checked) &&
     !(document.form1.x5c.checked) &&
     (document.form1.x5d.checked) &&
     !(document.form1.x5e.checked) &&
     !(document.form1.x5f.checked) &&
     (document.form1.x5g.checked) 
     )){alert("Your answer for f ''(x)<0 is incorrect.")}
  else 
  if (!(
     !(document.form1.x6a.checked) && 
     !(document.form1.x6b.checked) &&
     !(document.form1.x6c.checked) &&
     (document.form1.x6d.checked) &&
     !(document.form1.x6e.checked) &&
     !(document.form1.x6f.checked) &&
     !(document.form1.x6g.checked) 
     )){alert("Your answer for f '(x)=0 is incorrect.")}
  else 
  if (!(
     (document.form1.x7a.checked) && 
     (document.form1.x7b.checked) &&
     (document.form1.x7c.checked) &&
     (document.form1.x7d.checked) &&
     (document.form1.x7e.checked) &&
     (document.form1.x7f.checked) &&
     (document.form1.x7g.checked) 
     )){alert("Your answer for f increasing is incorrect.")}
  else 
  if (!(
     (document.form1.x8a.checked) && 
     !(document.form1.x8b.checked) &&
     !(document.form1.x8c.checked) &&
     !(document.form1.x8d.checked) &&
     !(document.form1.x8e.checked) &&
     !(document.form1.x8f.checked) &&
     !(document.form1.x8g.checked) 
     )){alert("Your answer for minima is incorrect.")}
  else 
     {alert("Your answers are CORRECT!")}
}