Question

what are critical points where f prime is 0??

on x^4/5(x+3)

Answer 1

u want to find the critical points of
\[ \large f(x)=\frac{x^4}{5(x+3)} \]
?

Answer 2

hello? ru there?

Answer 3

critical point is defined as where f' = 0 or f' does not exist

Answer 4

within the domain of f, of course....

Answer 5

noooo x^5/4

Answer 6

can you draw it?

Answer 7

noooo, i'm failing to

Answer 8

i mean use the "draw" button to show the function.....

Answer 9

x^4/5 * (x+3)

Answer 10

\[\huge f(x)=x^{\frac{4}{5}}(x+3) \]
like that?

Answer 11

x^4/5 * (x+3)

Answer 12

yes

Answer 13

http://graph-plotter.cours-de-math.eu/graph.php?a0=2&a1=x%5E4%2F5%20%2A%20%28x%2B3%29&a2=&a3=&a4=1&a5=3&a6=7&a7=1&a8=1&a9=1&b0=500&b1=500&b2=-10&b3=10&b4=-10&b5=10&b6=20&b7=10&b8=5&b9=5&c0=3&c1=0&c2=1&c3=1&c4=1&c5=1&c6=1&c7=0&c8=0&c9=0&d0=1&d1=20&d2=20&d3=0&d4=&d5=&d6=&d7=&d8=&d9=&e0=&e1=&e2=&e3=&e4=14&e5=14&e6=13&e7=12&e8=0&e9=0&f0=0&f1=1&f2=1&f3=0&f4=0&f5=&f6=&f7=&f8=&f9=&g0=&g1=1&g2=&g3=0&g4=0&g5=0&zalt=

Answer 14

there is the graph! open the link

Answer 15

i was not asking for the graph... i was asking that use the draw botton to write the function so that it would be clear what function we're talking about...

Answer 16

but we already have it , you confirmed it....

Answer 17

:(

Answer 18

best way to take the derivative here is to just multiply it out and use power rule, sum rule for derivatives...
\[\huge f(x)=x^{\frac{4}{5}}(x+3)=x^{\frac{4}{5}}\cdot x+x^{\frac{4}{5}}\cdot 3 \]
\[\huge f(x)=x^{\frac{9}{5}}+3x^{\frac{4}{5}} \]
can you take the derivative from here?

Answer 19

i got that part right... do i derive that?

Answer 20

yes...

Answer 21

what u got for the derivative?

Answer 22

mmm

Answer 23

9/5x^(4/5) + 12/5x^9(

Answer 24

+ 12/5x^9(

Answer 25

its freezing

Answer 26

the last part is 12/5x^(-1/5)

Answer 27

that last part should be + (12/5)x^(-1/5) , right?

Answer 28

ok... good...

Answer 29

next?

Answer 30

?

Answer 31

\[\huge f(x)=x^{\frac{4}{5}}(x+3)=x^{\frac{9}{5}}+3x^{\frac{4}{5}} \]
\[\huge f'(x)=\frac{9}{5}x^{\frac{4}{5}}+\frac{12}{5}x^{-\frac{1}{5}} \]
\[\huge f'(x)=\frac{9}{5}x^{\frac{4}{5}}+\frac{12}{5}x^{-\frac{1}{5}} = \frac{3(3x+4)}{5x^{\frac{1}{5}}}\]
ok... i just simplified your derivative...
set that equal to zero, what u got?

Answer 32

oh, btw, the graph you attached is NOT the graph of the function we're working on....

\(\large f(x) = x^{4/5}(x+3) \)