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I need help finding q'(7) where q(x) = f(x)/g(x) because:

F is a zig zag line and at x = 7 the coordinates are: (7,5) however the slope is negative on the left and positive on the right so I can't use your regular slope form to figure out how to find the derivative.

g(x)'s slope is .5 at the point, where the point is equal to (7, 2.5).

Verified Answer :

apologiabiology

remember the difference quotient
the deritivie of f(x)/g(x) is \(\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^2}\)
so
q'(7)=\(\frac{f'(7)g(7)-g'(7)f(7)}{(g(7))^2}\)
g(7)=2.5
g'(7)=0.5
f(7)=5
so
q'(7)=\(\frac{f'(7)(2.5)-(0.5)(5)}{2.5^2}\)
q'(7)=\(\frac{f'(7)(2.5)-2.5}{6.25}\)
now find the slope of f(x) at x=7
take the deritive and evaluate
(try googling a deritive calculator)
or just ask me

basically
the answer is \(\frac{f'(7)(2.5)-2.5}{6.25}\)
just find the slope of f(x) at x=7 (that is the slope at that specitific point, not for the whole graph)

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