3 Given the function fx 2x312x226x 2 find the x and y coord

3. Given the function f(x) 2x3-12x2+26x - 2, find the x and y coordinates of all inflection points. Inflection points are found by setting the second derivative equal to zero. 12-6 Copyright © 2015 Pearson Education, Inc.

Solution

1. f(x)=2x³-12x²+26x-2

f\'(x)= 6x²-24x +26

f\"(x)= 12x -24

Inflection point, f\"(x)=0

12x-24=0

x=2

f(2)=2(2)³-12(2)²+26(2)-2=22

Inflection point (2,22)

2. f(x)=2x⁵+7x^12/5+16

f\'(x) = 2*5x^5-1+ 7(12/5)x^{12/5 -1}+0 = 10x⁴+(84/5)x^7/5

f\"(x)= 10*4x^4-1+(84/5)(7/5)x^7/5-1= 40x³+ (588/25)x^2/5