Question

Evaluate the difference quotient for the given function. C%20%20%20f%284%2Bh%29-f%284%29%2Fh" id="TexFormula1" title="f(x)= x^{2} +1, f(4+h)-f(4)/h" alt="f(x)= x^{2} +1, f(4+h)-f(4)/h" align="absmiddle" class="latex-formula">

Answer 1

$\dfrac{f(4+h)-f(4)}h=\dfrac{((4+h)^2+1)-(4^2+1)}h=\dfrac{16+8h+h^2+1-16-1}h=\dfrac{8h+h^2}h=8+h$