Question

find the derivative x^1/4 (written as a square root), x=625

b) Find the equation of the tangent line at x=625

Answer 1

For my derivative, i had 1/4x^3/4
when i sub in 625, i get 1/500

is that right?

Answer 2

trying to get my y-value,

Answer 3

Lol...Didnt Get...u Find the Derivative of ---- ?

Answer 4

\[\sqrt[4]{x}\]

Answer 5

is what i need the derivative of, then i need to sub in 625 into the derivative to get x.

Answer 6

\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }}\]

\[\sqrt[4]{x} = x ^{\frac{ 1 }{ 2 }*\frac{ 1 }{ 4 }}\]

Answer 7

\[\frac{ d }{ dx }(x ^{\frac{ 1 }{ 8 }})\]

Answer 8

\[=\frac{ 1 }{ 8 }* x ^{\frac{ 1 }{ 8 }-1}\]

Answer 9

\[\sqrt[4]{x} = x^{1/4}\]

Answer 10

not a half times a quarter.

Answer 11

\[\frac{ 1 }{ 8 }*x ^{\frac{ -7 }{ 8 }} = \frac{ 1 }{ 8 }*\frac{ 1 }{ x ^{\frac{ 7 }{ 8 }} }\]

Answer 12

\[625 = 5^4\]

Answer 13

Hope nw u can solve...)

Answer 14

i dont get what you're doing here.

Answer 15

i got the derivative - \[\frac{ 1 }{ 4 }x ^{\frac{ -1 }{ 4 }}\]

Answer 16

and when i sub in 625, i get 1/500 as my x value for the equation.

Answer 17

that is not the \(x\) value, that is the slope

Answer 18

actually
\[\frac{1}{4\sqrt[4]{625}}=\frac{1}{4\times 2}=\frac{1}{20}\]

Answer 19

ooops i mean
\[\frac{1}{4\times 5}=\frac{1}{20}\]

Answer 20

oops still wrong derivative is
\[\frac{1}{4\sqrt[4]{x^3}}\] so you are correct, you get \(\frac{1}{500}\) as your slope

Answer 21

I don't think you guys are understanding my question.
I need to find the derivative of the given equation, then i have to find d/dx (625)
so i have to sub in 625 into my derivative,
so that gave me 1/500 for my slope.

so i then sub in 1/500 into the derivative equation to get my x value, then i'll sub that x value into my original equation to get my y value.

Answer 22

ok you have the function
\[f(x)=\sqrt[4]{x}\]
now \(f(625)=5\) so you know the point on the graph is \((625,5)\)
the slope is \(f'(625)=\frac{1}{500}\)
to find the equation of the line tangent to the curve at \((625,5)\) use the point slope formula and get
\[y-5=\frac{1}{500}(x-625)\]
you can clean that up with some algebra if you like, depending on what you need to do with it

Answer 23

that is the answer to the question
" Find the equation of the tangent line at x=625"

Answer 24

thank you,
sorry about the late delay... open study stopped working for me.