What is the first derivative and second derivative of #f(x) = (x-1)^2 (x-3)#?

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Answer 1 · 2018-06-27T08:11:42

#f'(x)=3(x-1)^2-4(x-1)#

#f''(x)=6x-10#

Let #u=x-1 , x-3=u-2 therefore (du)/dx=1#

#u^2(u-2)=u^3-2u^2#

#color(blue)(d/dx)(u^3-2u^2)#

#3u^2*(du)/dx-4u(du)/dx#

Substitute

#f'(x)=3(x-1)^2-4(x-1)#

#color(blue)(d/dx)(3u^2-4u)#

#6u(du)/dx-4(du)/dx#

Substitute

#f''(x)=6(x-1)-4=6x-10#