I'm not sure how to solve this problem.

Question

It says f(x) = 3x^2+2x+3. q(h) = (f(1+h)-f(1))/h. Then q(0.01) = ?  

Answer 1

The function f(x) = 3x² + 2x + 3

q(h) = [ f(1 + h) - f(1)]/h

• f(1 + h) = 3(1 + h)² + 2(1 + h) + 3

           = 3(1 + h² + 2h) + 2 + 2h + 3

          = 3 + 3h² + 6h + 2 + 2h + 3

          = 3h² + 8h + 8

• f(1) = 3(1)² + 2(1) + 3

                = 3 + 2 + 3

                = 8

q(h) = [ f(1 + h) - f(1)]/h

       = [ 3h² + 8h + 8 - 8 ]/h

       = (3h² + 8h)/h

       = h(3h + 8)/h

       = 3h + 8

q(0.01) = 3(0.01) + 8

            = 0.03 + 8

q(0.01) = 8.03