Find and simplify the difference quotient when f(x)= Square root of x?

Answer 1

d f(x) = 1/2*(1/sqrtx) *dx

Answer 2

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f(x) = √(x)
Formula:
f ‘ (x) = lim f(x+h) – f(x)
hào ----------------
h
So:
f ‘ (x) = √(x+h) - √(x)
--------------------
h
Get rid of radicals by multiplying the numerator
And denominator by same quantities with
A plus sign to square radicals.

Square Radicals
√(x+h) - √(x)
* [√(x+h) + √(x)]
------------------------
h * [√(x+h) + √(x)]
Multiply out numerator
x+h – x
= -------------
h * [√(x+h) + √(x)]
Combine the numerator
h
= --------------
h * [√(x+h) + √(x)]
Divide out the h
1
= --------------
[√(x+h) + √(x)]
@ h = 0
The denominator becomes:
1
= ------------
[√(x) + √(x)]
sum the denominator
Answer:
1
= -------------
2*√(x)

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