Find the exact location of all points of inflection of the...

Find the exact location of all points of inflection of the function. (Order your answers from smallest to largest x) g(x) = 2xe^(3x) (Write DNE in any unused blank) g has a point of inflection at (x,y) = (____,____) g has a point of inflection at (x,y) = (____,____)

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00:01 All right, so inflection points occur with the second derivative does not exist or is equal to zero.

00:05 So we're going to find the second derivative, but first we're going to find the first one.

00:08 So just consider this is your first function.

00:10 This is your second apply the product rule.

00:12 So 2x times the derivative of e to 3x, which is e to the 3x times 3, and then add e to the 3x times the 3x, which is 2x, and then add e to the 3x, which is 2x, and then you get g prime.

00:23 Or you can pull out of e to the 3x, and you're left with 2 times 3, which is 6x plus 2.

00:29 Now to find g double prime, let this be your first function, that be your second.

00:32 You get e to the 3x times the derivative of this, which is just 6, plus 6x plus 2, times 3, 8 to the 3x.

00:40 Once again, pull out an e to the 3x, and you get g2priam as e to 3x times the 3x times the quantity 6 plus 18x plus 6.

00:49 That's equal to e to 3x times 18x plus 12.

00:55 Now i'll say each one of these equal to 0, because this will exist everywhere.

00:58 8 to 3x actually never equals 0, so there's no solutions there.

01:01 But 8x plus 12 and most certainly equals 0, it actually equals 0, where 18x is equal to negative 12, so x is equal to negative 2 over 3.

01:10 This is a possible inflection point...

Question

Find the exact location of all points of inflection of the function. (Order your answers from smallest to largest x) g(x) = 2xe^(3x) (Write DNE in any unused blank) g has a point of inflection at (x,y) = (,) g has a point of inflection at (x,y) = (,)

Question

Find the exact location of all points of inflection of the function. (Order your answers from smallest to largest x) g(x) = 2xe^(3x) (Write DNE in any unused blank) g has a point of inflection at (x,y) = (____,____) g has a point of inflection at (x,y) = (____,____)

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Find the exact location of all points of inflection of the function. (Order your answers from smallest to largest x) g(x) = 2xe^(3x) (Write DNE in any unused blank) g has a point of inflection at (x,y) = (,) g has a point of inflection at (x,y) = (,)