Question

Evaluate the difference quotient for the given function. Simplify

Answer 1

f(x) = 1+2x-x^2

f(4+h) = 1+2(4+h)-(4+h)^2

          = 1+8+2h-(h^2+4^2+2(4)h)

           =-16-h^2-8h+1+8+2h

           =-7-h^2-6h

f(4) = 1+2(4)-(4)^2

        =1+8-16

           =-7

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[f(4+h)-f(4)]/[h] =[-7-h^2-6h-(-7)]/[h]

                        =[-h^2-6h)]/[h]

                         =-h(h+6)/h

                         =-(h+6)