Derivative of Average cost function

Question

In my last Maths test I needed the derivative of the average cost function of a quadratic cost function.

K(x) = ax² + bx + c

H(x) = (ax² + bx + c)/x ... average cost function

A programme we use in school states that the derivative is:

H'(x) = (-ax² - bx - c)/x²

but the actual derivative is

H'(x) = - c/x²

Am I wrong? Or my programme? Or are these derivative functions actually the same just in another form?

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Answer 1

Neither of those are correct for the derivative. Geogebra is interpreting $ax$ as a constant in cell 4, instead of $a \times x$. Try inputting Derivative(a x + b + c/x), with the space included. This would give you the correct derivative of $a - c/x^2$.

Similarly, Geogebra is interpreting $ax$ and $bx$ as constants in the expression for $K$. Add spaces there also.