Question

find k if f(x)=e^(x^2-k/x) has a relative min/max at x=2 HELP NEED TO CHECK MY ANSWER FAST THANK YOU

Answer 1

and your answer is?

Answer 2

first derivative

set to zero

subsitute x=2

solve for k

voila

Answer 3

I think that I did the derivative incorrectly now

Answer 4

chain rule

Answer 5

I know that e^x = e^x

Answer 6

right,
and?

Answer 7

I am good at implicit differentiation but the e confuses me

Answer 8

is it e as is and then the derivative of the exponent?

Answer 9

yup

Answer 10

so I did e^(x^2-k/x) then it is 2x and then I am stuck

Answer 11

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

Answer 12

Sorry. I am lost

Answer 13

derivative of x^n is \[nx^{n-1}\]

Answer 14

k is a constant

Answer 15

ok so that explains the 2x right. The k/x is confusing

Answer 16

n= -1

Answer 17

I don't believe it is quotient rule

Answer 18

k/x = k x^-1

Answer 19

\[y \prime= e ^{x^2-K/x} \times 2x(kx^-1\] ?

Answer 20

nope

Answer 21

just focus on doing the derivative of this

x^2-k/x

Answer 22

(x^2-k/x)' = 2x -(k/x) '

Answer 23

k/x = kx^-1

Answer 24

(kx^-1)'

tell me a good reason why you cant apply

\[nx^{n-1}\]

to that?

Answer 25

does that turn into kx^-2?

Answer 26

dont forget the n in front

Answer 27

-kx^-2

Answer 28

ohhh

Answer 29

ok so then the derivative of
x^2-k/x is ????

Answer 30

2x+kx^-2?

Answer 31

and kx^-2 is?

Answer 32

well its k/x^2

Answer 33

but yes you have it right

Answer 34

haha I'm understanding this but can you help me put this together

Answer 35

what do you still not understand?

Answer 36

so the derivative is 2x+k/x^2?

Answer 37

yup

Answer 38

derivative of
x^2 -k/x is
2x+k/x^2

Answer 39

what I have now is e^(x^2-k/x) x 2x+k/x^2

Answer 40

e^(x^2-k/x) (2x+k/x^2)

dont use x as a multiplication sign, it can be easily mistaken as a variable

use * instead or parenthesis, but yes

Answer 41

now for the second part of the question. if the relative min/max is at x=2 what Should I do

Answer 42

relative max/min occurs when f'(x) = 0

Answer 43

Now like @completeidiot said, we know the derivative is 0 at x = 2 so substitute for x = 2 and set the whole thing to equal 0 and solve for k.

@soccerboy43

Answer 44

hi genius, am i taking too long :P

Answer 45

na its ok. take ur time. u still got 257 days, 3 hours, and 27 seconds.

Answer 46

plug 2 in for all x values?

Answer 47

till?

Answer 48

yes

Answer 49

till this thing ends.

Answer 50

made up number?

Answer 51

ya lawl. i think u missed the joke there...

Answer 52

i think i did

Answer 53

I have e^(4-k/4) times 4 + (2/x)^2

Answer 54

you forgot an x