Question

Find an equation of the tangent line to the graph of f at the given point:

Answer 1

\[f(x)=x+\frac{ 4 }{ x }, (4,5)\]

Answer 2

I'm just having trouble finding the derivative

Answer 3

I suggest you write the equation as:
\[f(x)=x+4x^{-1}\]
\[\large f'(x)=1-\frac{4}{x^{2}}\]

Answer 4

can you explain why?

Answer 5

When you rewrite the equation as above, you can then differentiate by using the usual rule for differentiation.

Answer 6

is there a formula for that?

Answer 7

The rule for differentiation of powers of x is:
\[\large f(x)=x^{n}\rightarrow\ f'(x)=nx^{n-1}\]

Answer 8

Have you studied Calculus?

Answer 9

I am currently studying the course

Answer 10

can you explain how the denominator became part of the numerator

Answer 11

Do you understand that:
\[\large \frac{1}{x}=x^{-1}\]

Answer 12

yeah

Answer 13

how did the x^2 get on bottom

Answer 14

Power Rule
\[\Large f(x) = x^n\]
\[\Large f \ '(x) = nx^{n-1}\]
where n is a constant

Answer 15

In this case, n = -1

\[\Large f(x) = x^{-1}\]
\[\Large f \ '(x) = -1x^{-1-1}\]
\[\Large f \ '(x) = -1x^{-2}\]
\[\Large f \ '(x) = -\frac{1}{x^{2}}\]

Answer 16

Then you find gradient :
m = f'(4)
\[m = 1 - \frac{ 4 }{ x^2 }\]

Then, you just need to input (x,y)
(y - y1) = m (x -x1)
(y - 5) = m (x - 4)

Done..........

Answer 17

Determine the equation of surface which is formed by the tangents of ellipsoid x^2 + y^2/2+z^2=1. Also that surface contain point M(5,5,5).
Help me with this.
It is the same problem.

Answer 18

sorry I can't @canimcan

Answer 19

still need help

Answer 20

with what?

Answer 21

i don't understand where x^2 came from and how it became the denominator

Answer 22

ok, go steps
f(x) = x+4/x
hey, you need stay to get help. If you leave, I leave too.

Answer 23

Now, derivative of f(x) =?

Answer 24

1 +?

Answer 25

ok, tell me 4/x =??

Answer 26

\(\dfrac{4}{x}=4x^{-1}\) ok?

Answer 27

yeah i understand up to that point

Answer 28

Now, take derivative of it. Apply the n rule.