Question

Find the difference quotient of ​f(x)equals=x squared plus 1x2+1​; that is find startfraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over h endfraction f(x+h)−f(x) h​, hnot equals≠0.

Answer 1

For f(x) = x² +1, the difference quotient (q) is
   q = (f(x+h) -f(x))/h

   q = ((x+h)²+1 - (x²+1)/h
   q = (x² + 2hx + h² + 1 - x² - 1)/h
   q = h(2x +h)/h
   q = 2x +h