Question

@zepdrix if f(x)=(x)sqrt(5-x) find f'x
find equations to the curve y=(x)sqrt(5-x) at the points (1,2) and (4,4)

Answer 1

2 separate tangent line equations? :D hmm ok.
If we're able to find the derivative effectively, then this problem will be a piece of cake.

Answer 2

are we using chain rule here?

Answer 3

\[\huge f(x)=x \sqrt{5-x}\]
Hmm we have the product of two functions of x (two thingies with x in them). So we'll need to apply the product rule.

Answer 4

If you don't know the derivative of the square root, then make sure you rewrite it as a fractional exponent before differentiating.

Answer 5

question if it was just \[\sqrt{5-x}\] then we would use chain rule right?

Answer 6

Yes.

Answer 7

Ooo I finally got level 75, yay! :D lol

Answer 8

so we get with the product rule, x(1/2(5-x)^-1/2(-1))+(sqrt(5-x)(1)

Answer 9

congrats!

Answer 10

Ok derivative looks good.

Answer 11

Now that you've taken the derivative, you might want to put it in a form that's easier to work with before we plug the numbers in.
It doesn't matter if you do or not, but I always find square roots easier to read the 1/2's.

Answer 12

x(-1/2(5-x)^-1/2)+(sqrt(5-x)

Answer 13

read THAN 1/2's* typo

Answer 14

right so that is x(-1/2(1/sqrt(5-x))+(sqrt(5-x))

Answer 15

x(-1/2sqrt{5-x}\] +(sqrt(5-x))

Answer 16

Equation tool giving you trouble? :) hehe

Answer 17

So now we just plug in our values yes? c:

Answer 18

okay so we plug in the y value for (1,2) and (4,4)?

Answer 19

We don't care about y values. (remember in the previous problem we did? We used the y value for our final setup. But we don't care about it for any of the rest of the problem).
Just plug in the x value :)

Answer 20

Now if we get to a problem that requires us to differentiate IMPLICITLY, then yes, we'll have to use the y value. But we haven't run into a problem like that yet c:

Answer 21

okay so 1/2sqrt(2)+sqrt(2)

Answer 22

water you doing? D: How did you get a 2 under the square root.
Neither 5-1 nor 5-4 produce 2.. hmm

Answer 23

okay I had 1(1/2sqrt(5-1)) + (sqrt(5-1)

Answer 24

oh oh i see, so you didn't have the square root anymore :D k fair enough

Answer 25

5-1 is 4 sqrt of 4 is 2 right?

Answer 26

what happened to the negative sign on the first term?
Watch those little things mr/ms! >:O

Answer 27

ohhhhhhhhh crap

Answer 28

-1/4+ 2

Answer 29

9/4

Answer 30

mmmmm close :\ watch those fractions now! :OO

Answer 31

7/4

Answer 32

yay, so whats the equation for the first tangent line? :D

Answer 33

y-2=7/4(x-1)

Answer 34

yay

Answer 35

and then we just plug in 4 for the second tangent line

Answer 36

I got three for the slope of the second tangent line which gives us y-4=3(x-4)

Answer 37

Hmm did you forget the minus sign again? I think the slope is suppose to be -1.

Answer 38

yup you are right