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anonymous
 3 years 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
anonymous
 3 years 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@electrokid can u help?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0using our previous discussions, you can start the work and I guide.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0step 1) first derivative \(y'=?\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry i replied late i had internet issues. but the first derivative is 4x^2(x + 3)

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay i got x = 3 and x = 0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0good. those are the critical points. step 3) classify as maxima, minima or neither step 3.1) find second derivative of "f" > find f''(x)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0are u there @electrokid

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0step 3.1) find the second derivative.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Remember 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so i substitute those critical point into the second derivative

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes. \(f''(x)=12x^2+24x\) step 3.2) plug in x=3 in this equation and check the sign..

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and when i plugged in 0 i got 0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, so, f''(3) = 36 This is positive, therefore...?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0a local minimum ;) What about f''(0) ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's neither positive nor negative, right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well, what does that mean, then?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so it will be neither

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It will be neither :D

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@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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