Question

Determine the critical #s, the intervals on which the function is increasing or decreasing, all relative maximum points and relative minimum points, and the intervals of concavity.

f(x)= (x^2+4) / (x-8)^2

Answer 1

For which function ????

Answer 2

oh sorry!

f(x)= (x^2+4)/(x-8)^2

Answer 3

Any work on this so far ?

Answer 4

uh yea i did the derivative and got something like 2(x-x^2+4) but idk it ocudl be wrong

Answer 5

Let's use Equation Editor to express your function.\[f(x)= (x^2+4)/(x-8)^2=\frac{ x^2+4 }{ (x-8)^2 }\] Don't have to do this, but seeing the function in this form makes it so much clearer, for me, anyway.

This is a quotient function

To find its derivative, apply the quotient rule. Are you familiar with that?

Answer 6

Here to find derivative we need to use quotient rule of differentiation Are you familiar with it ???

Answer 7

(Great minds think alike! :) )

Answer 8

uh i think

Answer 9

im not sure

Answer 10

what i did was the deonominator and the derivative of the numerator and then vice versa

Answer 11

Suggest you make up a list of common derivative formulas and refer to it often.

The Quotient Rule is \[\frac{ d }{ dx }\frac{ f }{ g }=\frac{ g*f ' - f*g }{ g^2 }\]

Answer 12

yea thats wat i did

Answer 13

the answer i got was 2x-2(x^2-4)/(x-8) and then i triedd simplifying it more

Answer 14

then, replacing the functions f and g and their derivatives in this formula by their values in the given problem, \[\frac{ d }{ dx }\frac{ f }{ g }=\frac{ (x-8)^2*2x - (x^2+4)*2(x-8)^1 }{ ((x-8)^2)^2 }\]

Answer 15

Please simplify this as much as you can.

Answer 16

Just to be clear: f(x)=x^2+4
f' (x) = 2x
g(x)=(x-8)^2
g'(x)=2(x-8)

Answer 17

You need to find the "critical values" and then the corresponding "critical points." To do this, set the numerator of the derivative = to 0 and solve for x.

Were I doing this, I would factor out (x-8) from the numerator first.

Answer 18

yes thats wat i did

Answer 19

i think. my answer was 2x-2(x^2-4)/(x-8)

Answer 20

Please explain. Was this expression your derivative, the numerator of the derivative, the denominator, or what? It's really hard to communicate these expressions through ordinary typing; if you were to use Equation Editor or Draw, your intent would be clearer.

Answer 21

is that better?