Question

Let f(x)=sqrt(3x-6)
Find f(14+h)=
Find f(14)=
Find f(14+h)-f(14)=
Find (f(14+h)-f(14))/h=
Use algebra to simplify the expression so that you can take the limit as . Right now if take that limit then you would wind up with the indeterminant form . Hint: h should only appear once in your simplified expression.
Find f'(14)=(f(14+h)-f(14))/h as the limit of h approaches 0.

Answer 1

So far I have: f(14+h)=sqrt(36+3h)
f(14)=6
f(14+h)-f(14)=sqrt(36+3h)-sqrt(36)

But I can't figure out the last two.

Answer 2

f(14 + h) is simply the function with x replaced with 14 + h

so



the last two would be
f(14+h)-f(14)=


sqrt(3(14+h)-6) - sqrt(3(14)-6)

((f(14+h)-f(14))/h=
( sqrt(3(14+h)-6) - sqrt(3(14)-6) )/h
this last one is important as it is the definition of a derivative I recommend memorizing it!

Answer 3

A simple example
f(x) = 3x
thus
f(x+b+c+d) = 3(x+b+c+d)

Answer 4

hope this helps

Answer 5

this is simple buddy

Answer 6

all you have to do is multiply the numerator with its conjugate

Answer 7

so the equation reduces to \[[ (36+3h)-36 ]\div(h (\sqrt{36+h}+6)\]

Answer 8

now you can reduce the equation to \[3h \div(h \times(\sqrt{36+h} +6))\]

Answer 9

h from numerator & denominator cancels. now you can directly apply the limits(put h=0) to find out the derivative

Answer 10

also try to memorize the last equation as it is the first definition of derivative

Answer 11

Most of the Mathematica attachment answers your questions.