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 one year ago
Find all critical numbers and use the First Derivative Test to classify each as the location of a location maximum, local minimum, or neither. y = x^4 + 4x^3  2
 one year ago
Find all critical numbers and use the First Derivative Test to classify each as the location of a location maximum, local minimum, or neither. y = x^4 + 4x^3  2

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onegirl
 one year ago
Best ResponseYou've already chosen the best response.1@electrokid can u help?

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1using our previous discussions, you can start the work and I guide.

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1step 1) first derivative \(y'=?\)

onegirl
 one year ago
Best ResponseYou've already chosen the best response.1Sorry i replied late i had internet issues. but the first derivative is 4x^2(x + 3)

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1good. step 2) solve for "x": \(4x^2(x+3)=0\)

onegirl
 one year ago
Best ResponseYou've already chosen the best response.1okay i got x = 3 and x = 0

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1good. those are the critical points. step 3) classify as maxima, minima or neither step 3.1) find second derivative of "f" > find f''(x)

onegirl
 one year ago
Best ResponseYou've already chosen the best response.1are u there @electrokid

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1step 3.1) find the second derivative.

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Remember the critical points that you got? If the second derivative is positive when evaluated at one of those critical points, that critical point would be a local minimum. On the flipside, if the second derivative is negative when evaluated at a critical point, that point would be a local maximum.

onegirl
 one year ago
Best ResponseYou've already chosen the best response.1so i substitute those critical point into the second derivative

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1yes. \(f''(x)=12x^2+24x\) step 3.2) plug in x=3 in this equation and check the sign..

onegirl
 one year ago
Best ResponseYou've already chosen the best response.1and when i plugged in 0 i got 0

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Okay, so, f''(3) = 36 This is positive, therefore...?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2a local minimum ;) What about f''(0) ?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2It's neither positive nor negative, right?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Well, what does that mean, then?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2It will be neither :D

electrokid
 one year ago
Best ResponseYou've already chosen the best response.1@PeterPan and @onegirl both did a great job and effort and both deserve a medal :) so, @onegirl give one to PPan ☮
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