Question

Find all values of x (if any) where the tangent line to the graph of the given equation is horizontal.

f(x) = 7x − 7 ( square root ) x

Answer 1

Did you find the 1st Derivative of f(x)? That would be a good place to start.

Answer 2

y' = 7 - 1 / 7 root x?

Answer 3

Not quite. How did that '7' get in teh denominator? \[y' = 7 - \frac{ 7 }{ 2\sqrt{x} }\] Let's make sure we know where that came from.

Answer 4

ohh i see, so the next step would be to set the equation to 0, correct? then solve?

Answer 5

Let's see what you get.

Answer 6

i got 49/4 for my answer

Answer 7

You'll have to show me that result. You wandered off, somewhere.

Answer 8

7- 7\[7 - \frac{ 7 }{ 2\sqrt{x} }= 0\]

Answer 9

\[2\sqrt{x}= 7\]

Answer 10

\[\sqrt{x}^2 = ( \frac{ 7}{ 2 })^2\]

Answer 11

then i got 49/4

Answer 12

ok that isnt correct. what did i do wrong?

Answer 13

Yeah, ...no. Let's get that algebra up to speed.

\[7 - \frac{7}{2\cdot\sqrt{x}} = \frac{14\cdot\sqrt{x} - 7}{2\cdot\sqrt{x}}\]

Answer 14

what would my next step be?

Answer 15

\[\frac{ 7(2\sqrt{x}-1) }{ 2\sqrt{x} }=0\]\[2\sqrt{x}-1=0\]\[x=(\frac{ 1 }{ 2 })^{2}=1/4\]

Answer 16

@chrislb22 Did you get it?

Answer 17

yes i did, however someone else wrote a different solution

Answer 18

if you scroll up a couple convos, theres a different layout, which one is correct?

Answer 19

@Zekarias

Answer 20

who?

Answer 21

tkhunny, not sure if you can see it, but a few convos up

Answer 22

That person gives you the correct step.

Answer 23

i see

Answer 24

hey thanks a lot for your help

Answer 25

I think the most important part of this particular discussion was this: "Let's get that algebra up to speed."

Seriously, you can learn a whole lot more about the calculus if you don't spend half your study time fighting with algebra.