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f(x) = 3x^4 - 8x^3 + 6x^2         Find the derivative of the function

f'(x) = 12x^3 - 24x^2 +12x       The critical values are the f' set = 0

 

12x^3 -24x^2 + 12x  = 0              

12x(x^2 - 2x + 1) = 0               factor out 12x

12x (x - 1) (x - 1) = 0               factor the x^2 factor

12x = 0 , x - 1 = 0

x = 0 , x = 1

restating the f'

f'(x) = 12x^3 - 24 x^2 + 12x   find the second derivative

f"(x) = 36x^2 - 48x + 12

f"(0) = 12 positive   that means there is a min at x = 0.

f"(1) = 36(1) - 48(1) + 12 = 36 -48 + 12 = 0  at x = 1 there is a invertion point.

by Level 10 User (55.7k points)

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