Find-the-optimum-points-of-the-function-y-f-x-f-x-2x-3-3x-2-36x-34-

Question Number 32776 by NECx last updated on 02/Apr/18

F i n d t h e o p t i m u m p o i n t s o f

t h e f u n c t i o n y = f (x)

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 34

Answered by MJS last updated on 02/Apr/18

f^{'} (x) = 0 \land f^{″} (x) > 0 \Rightarrow m i n

f^{'} (x) = 0 \land f^{″} (x) < 0 \Rightarrow m a x

f^{'} (x) = 6 x^{2} - 6 x - 36

f^{″} (x) = 12 x - 6

f^{'} (x) = 0

x^{2} - x - 6 = 0

x = \frac{1}{2} \pm \sqrt{\frac{1}{4} + 6} = \frac{1}{2} \pm \sqrt{\frac{25}{4}} =

= \frac{1}{2} \pm \frac{5}{2} \Rightarrow x_{1} = - 2; x_{2} = 3

f^{″} (- 2) = - 30 \Rightarrow m a x = (\begin{matrix} - 2 \\ 78 \end{matrix})

f^{″} (3) = 30 \Rightarrow m i n = (\begin{matrix} 3 \\ - 47 \end{matrix})

Commented by NECx last updated on 02/Apr/18

t h a n k y o u s o m u c h

Facebook Tweet Pin