Math 2003 review Test C -26

Let g be the function defined by g(x)=x^3-x-2. Then (g(3+h)-g(3-h))/(2h)=?

The function is g(x)  =  x^3 - x - 2

Substitute x = (3 + h) in g(x)

g(3 + h)  =  (3 + h)^3 - (3 + h) - 2

=  27 + 27h + 9h^2 + h^3 - 3 - h - 2

=  22 + 26h + 9h^2 + h^3

Substitute x = (3 - h) in g(x)

g(3 - h)  =  (3 - h)^3 - (3 - h) - 2

=  27 - 27h + 9h^2 - h^3 - 3 + h - 2

=  22 - 26h + 9h^2 - h^3

(g(3+h)-g(3-h))/(2h)  =  [ (22 + 26h + 9h^2 + h^3) - (22 - 26h + 9h^2 - h^3) ] / 2h

=  [ 22 + 26h + 9h^2 + h^3 - 22 + 26h - 9h^2 + h^3 ] / 2h

=  [ 26h+ h^3 + 26h + h^3 ] / 2h

=  [ 52h+ 2h^3 ] / 2h

=  2h[ 26+ h^2 ] / 2h

=  26 + h^2

(g(3+h)-g(3-h))/(2h)  =  26 + h^2.

Thank you. I did the same and I have the same result, but my professor said that the answer is wrong. He said that the result should be

(g(3+h)-g(3-h))/(2h)=x-(1/2)

I don't know how he gets this answer.

Thank you very much for your help.

Thank you. I did the same and I have the same result, but my professor said that the answer is wrong. He said that the result should be

(g(3+h)-g(3-h))/(2h)= 5

I don't know how he gets this answer.

Thank you very much for your help.

Correction for my previous comment.

Thank you. I did the same and I have the same result, but my professor said that the answer is wrong. He said that the result should be

(g(3+h)-g(3-h))/(2h)= 5

I don't know how he gets this answer.

Thank you very much for your help.

I am cross checked the answer same answer come to me also