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secondary 4 | A Maths

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Good afternoon! How do i do qns 35? Just part i will do :)

Another way is to do long division and reasoning.

y = (16 - 3x) / (x + 3)

dy/dx

= (x + 3) (-3) - (16 - 3x) (1), whole thing divided by (x + 3)^2

= -9 divided by (x + 3)^2

(x + 3)^2 is always non negative but here it cannot equal zero since it is in denominator

So dy/dx < 0 for all x except 3

*correction to previous line: except -3*

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For a decreasing function, show dy/dx is always negative for all relevant values of x.