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Find any intercepts, relative extrema, and points of inflection. Then enter DNE.) y = 3x^4 + 4x^3 intercept (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value) relative minimum (x, y) = ( ) relative maximum (x, y) = ( ) points of inflection (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value)

          Find any intercepts, relative extrema, and points of inflection. Then enter DNE.)
y = 3x^4 + 4x^3
intercept (x, y) = ( ) (smaller x-value)
(x, y) = ( ) (larger x-value)
relative minimum (x, y) = ( )
relative maximum (x, y) = ( )
points of inflection (x, y) = ( ) (smaller x-value)
(x, y) = ( ) (larger x-value)

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Find any intercepts, relative extrema, and points of inflection. Then enter DNE.)
y = 3x^4 + 4x^3
intercept (x, y) = ( ) (smaller x-value)
(x, y) = ( ) (larger x-value)
relative minimum (x, y) = ( )
relative maximum (x, y) = ( )
points of inflection (x, y) = ( ) (smaller x-value)
(x, y) = ( ) (larger x-value)

Added by Carolina R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kathleen Carty

07/13/2023

Step 1

First, we find the first and second derivatives of the given function: Given function: $y = 3x^4 + 4x^3$ Show more…

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Find any intercepts, relative extrema, and points of inflection. Then enter DNE.) y = 3x^4 + 4x^3 intercept (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value) relative minimum (x, y) = ( ) relative maximum (x, y) = ( ) points of inflection (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value)

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Transcript

00:01 So i have y equals 3x to the fourth plus 4x cubed.

00:07 I first want to find intercepts.

00:12 X intercepts happen when your function equals 0.

00:17 So i'm going to factor out an x cubed.

00:21 That gives me 3x plus 4.

00:25 So i have x cubed is 0, 3x plus 4 is 0.

00:29 So i have 0 and negative 4 thirds.

00:34 As coordinates, that's negative 4 thirds, 0 and 0, 0.

00:40 Next i want to find relative min or max.

00:45 So i'm going to find the derivative, which is 12x cubed plus 12x squared.

00:55 I'm going to set that equal to 0 and i'm going to factor out a 12x squared.

01:01 That leaves me with x plus 1.

01:04 So i have critical values at 0 and negative 1.

01:09 I'm going to plot them on a number line.

01:12 Then i'm going to take my derivative, 12x cubed plus 12x squared.

01:22 And i'm going to choose some test points.

01:32 So if i plug in negative 2, i get out something negative.

01:38 Negative 1 half, i'm going to get out something positive.

01:42 And 1, i'm going to get out something positive.

01:48 Okay, so that tells me i'm going to have a relative min.

01:54 I'm decreasing here and then i'm increasing here.

01:57 So i'm going to have a relative minimum at negative 1...

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