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).
remember the difference quotient the deritivie of f(x)/g(x) is [tex] \frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^2} [/tex] so q'(7)=[tex] \frac{f'(7)g(7)-g'(7)f(7)}{(g(7))^2} [/tex] g(7)=2.5 g'(7)=0.5 f(7)=5 so q'(7)=[tex] \frac{f'(7)(2.5)-(0.5)(5)}{2.5^2} [/tex] q'(7)=[tex] \frac{f'(7)(2.5)-2.5}{6.25} [/tex] 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 [tex] \frac{f'(7)(2.5)-2.5}{6.25} [/tex] just find the slope of f(x) at x=7 (that is the slope at that specitific point, not for the whole graph)
