For the function: F(x)= square root (7x+22) compute the difference quotient : [F(x+h)-f(x)] h H isn't equal to 0. Attempt to simplify your answer.
once you get to \[\frac{\sqrt{7x+7x+22}-\sqrt{7x+22}}{h}\] you may think "what else is there to do?" you can simplify this a great deal by "rationalizing the numerator" i.e. multiplying by \[\frac{\sqrt{7x+7h+22}+\sqrt{7x+22}}{\sqrt{7x+7h+22}+\sqrt{7x+22}}\]
would it be absolutely wrong to try and solve it by turning the radical polynomials into (...)^(1/2) then solve?
typo in first line it should be \[\frac{\sqrt{7x+7h+22}-\sqrt{7x+22}}{h}\]
yes, it will not help your cause at all to use rational exponents. just a different way to write it
if you write what i suggested, you will end up with 7h in the numerator, and will be able to cancel the h in the numerator and denominator
yeah when it comes to the definition of a derivative ... it seems like i don't even know the basic rules haha. I'm overwhelmed I guess. Yeah , i got "7" and its wrong
you will get \[\frac{7h}{h(\sqrt{7x+7h+22}+\sqrt{7x+22})}\]
then \[\frac{7}{\sqrt{7x+7h+22}+\sqrt{7x+22}}\]
and if you are supposed to let h go to zero you will end up with \[\frac{7}{2\sqrt{7x+22}}\]
thanks, I guess i just need to calm myself while doing it and not think its overwhelming... just apply what I know situation.
I have a question if i get a F(x): 12/(x+30) and I were to use the definition of a derivative would I have to get a common denominator for the top and do all that math? or is there a trick?
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