Question

difference quotient for radical 7x+5

Answer 1

\[f(x) = \sqrt{7x + 5}\] then \[f(x+h) = \sqrt{7(x+h) +5} = \sqrt{7x +7h + 5}\] now subtract f(x) from f(x+h) to get \[f(x+h) - f(x) = \sqrt{7x + 7h + 5} - \sqrt{7x + 5}\] now divide both sides by h to get \[[f(x+h)-f(x)]/h = [\sqrt{7x+7h+5} - \sqrt{7x+5}]/h\] from here, it's going to get a little messy because you will need to multiply the numerator and denominator by \[[\sqrt{7x+7h+5} + \sqrt{7x+5}\] this is called the conjugate. you will have to do some simplification, then apply h approaching zero to get \[[f(x+h)-f(x)]/h = 1/(2\sqrt{7x+5})\] let me know if you need further assistance.

Answer 2

i appreciate all the work, but i think your final solution is wrong

Answer 3

i forgot the 7...the answer should be \[7/(2\sqrt{7x+5})\]

Answer 4

that is still incorrect

Answer 5

let me put it another way...\[(7/2)(\sqrt{7x+5})^{-1/2}\]

Answer 6

if it is still wrong...please, rewrite the equation using equation editor

Answer 7

difference equation of f(x)=\[\sqrt{7x+5}\]

Answer 8

what solution are you getting...

Answer 9

\[\sqrt{7h}/5\]

Answer 10

have you covered derivatives?

Answer 11

yes, is difference quotient a derivative cuz then i could bypass all this stupid (x+h) stuff

Answer 12

what i did is basically took the derivative of f(x)...that is the result. difference quotient will eventually turn out to be derivative later on...most likely the next section or chapter.

Answer 13

ok, i will just try to do it as a derivative then
thank you

Answer 14

yw