Question

SOMEONE PLEASE HELP!!! Find and simplify the difference quotient f(x + h) − f(x)/h for the following function. (Hint: Rationalize the numerator.) f(x) = 8 square root of x

Answer 1

this is due by midnight please help!

Answer 2

are you sure its f(x+h) - f(x)/h? just checking.

Answer 3

yep thats the exact equation

Answer 4

do you have answer choices? cause there really isnt much you can do with this

Answer 5

unfortunantly i dont:( i cant find how to do this problem anywhere

Answer 6

if it helps, its supposed to look like f(x)=\[8\sqrt{x}\]

Answer 7

What do you mean?

Answer 8

i wrote f(x)= 8 square root of x, and im just showing it how it actually looks which is \[8\sqrt{x}\]

Answer 9

Oh ok. Well the best that I can give you is this\[\frac{ 8h \sqrt{x+h} -8\sqrt{x} }{ h }\]

Answer 10

Sorry. I really dont see another way for it to be simplified

Answer 11

\[\frac{ 8\sqrt{x+h} -8\sqrt{x}}{ h }\]
now multiply by the conjugate

Answer 12

what is the conjugate?

Answer 13

\\[\frac{ 8\sqrt{x+h}-8\sqrt{x} }{ h }\times \frac{ 8\sqrt{x+h}+8\sqrt{x} }{ 8\sqrt{x+h}+8\sqrt{x} }\]

Answer 14

so then what would i do next

Answer 15

\[\frac{ (8\sqrt{x+h)}^2-(8\sqrt{x} ^2}{ h(8\sqrt{x+h}+8\sqrt{x} }\]
so what happens when u square a square root ?

Answer 16

it cancels the square root?

Answer 17

yup so what would u be left with

Answer 18

8x^2+16xh+8h^2-8x^2

Answer 19

theres your answer