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OpenStudy (anonymous):

if a and b are nonzero constants, find the domain and all critical points of f(x)= (ax^2)/(x-b) if a and b are nonzero constants, find the domain and all critical points of f(x)= (ax^2)/(x-b) @Mathematics

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myininaya (myininaya):

\[\text{all real numbers,} x \neq b \]

myininaya (myininaya):

use the quotient rule to find f'

myininaya (myininaya):

\[f'(x)=\frac{(ax^2)'(x-b)-ax^2(x-b)'}{(x-b)^2}=\frac{2ax(x-b)-ax^2(1-0)}{(x-b)^2}\] \[=\frac{2ax^2-2axb-ax^2}{(x-b)^2}=\frac{ax(2x-2b-x)}{(x-b)^2}=\frac{ax(x-2b)}{(x-b)^2}\] when is the numerator 0? when ax=0 or when x-2b=0 solve both for x and voolah critical numbers also you can say x=b is a critical number since f' dne exist there

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