Question

Over which interval does the function decrease the fastest? when f(x)=3rd power sqreroot(-x+5)

Answer 1

pleaseeeeeee help anyoneee

Answer 2

its 330 am its my last math problem I can't get it wrong and I can't solve on my own

Answer 3

did you take the derivative twice

Answer 4

what do you mean, no I don't think so.

Answer 5

the second derivative will tell you on which interval it is decreasing the fastest

Answer 6

the first derivative will tell you on which interval it is decreasing

Answer 7

second derivative also tells you instantaneous velocity at a point. :-)

Answer 8

Oh ok well I wasn't taught what the second one was hoe do I get it? like how to solve for it?

Answer 9

I'm guessing the 4th derivative (imaginary) will tell you when it's decreasing at light speed! aha.

Answer 10

Were you taught the first derivative?

Answer 11

I don't know how to solve this eqaution at all could you tell me what steps to take first?

Answer 12

okok, are you taking calculus right now? Or is this just algebra?

Answer 13

its algebra statistics

Answer 14

Ohh.... hmm Im not too sure. @perl

Answer 15

I think she left thanks for looking @Jhannybean

Answer 16

hmm...maybe maybe not!

Answer 17

the function is
f(x) = (-x+5)^(3/2) , correct?

Answer 18

My reasoning was:
sqrt(-x + 5)^3 = [(-x+5)^(1/2) ] ^3 = (-x+5)^(3/2 )

Answer 19

Note that the function is only defined for x <= 5 , since the expression under the square root must be greater than or equal to zero.

f ' (x) = 3/2 * (-x + 5) ^(1/2) * (-1)
f ' (x) = -3/2 (-x+5)^(1/2)
critical points are x = 5

so f is decreasing for x <= 5

f ' ' (x) = -3/2 (-x + 5) ^(-1/2) (-1)
f ' ' (x) = 3/2 (-x+5)^(-1/2)
it is concave down for x <= 5

Since f is decreasing and concave down
it is decreasing the fastest when x = -infinity

There might be a typo in your question, since the answer is kind of strange. Or I misunderstood the question.

Answer 20

@sandysparklesblahhhhhhh maybe you could upload the original question , take a screen shot

Answer 21

second derivative is speed? Where you get that Jhanny?

Answer 22

The first derivative will tell you the rate it is decreasing.
The second derivative will tell you the critical points of the first derivative, so that you can minimize the first derivative.