Final answer:
Using the quotient rule for differentiation, the derivative of h(x)/x evaluated at x=2 is calculated to be -6.5.
Step-by-step explanation:
To find d/dx(h(x)/x) evaluated at x=2, we can use the quotient rule for differentiation. The quotient rule states that the derivative of a function in the form of u/v is (v*u' - u*v')/v^2, where u and v are functions of x, and u' and v' are their respective derivatives.
Let's let u = h(x) and v = x. The derivatives are u' = h'(x) and v' = 1. Substituting in the given values, we have u(2) = h(2) = 8 and u'(2) = h'(2) = -9. Since v = x, we have v(2) = 2 and v'(2) = 1.
Now applying the quotient rule, we find:
d/dx(h(x)/x)|x=2 = (2*(-9) - (8*1)) / (2)^2
= (-18 - 8) / 4
= -26 / 4
= -6.5
Thus, the derivative of h(x)/x evaluated at x=2 is -6.5.