Derieving Derivative #5

Calculus Level 2

The local minimum of 2 x 3 − 3 x 2 − 12 x + 8 2x^3-3x^2-12x+8 occurs at x =

4 3 2 -1

Parag Zode by Parag Zode , 24, India

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2 solutions

Parag Zode
Aug 26, 2014

f ( x ) = 2 x 3 − 3 x 2 − 12 x + 8 f(x)=2x^3-3x^2-12x+8 so , f ′ ( x ) = 6 x 2 − 6 x − 12 = 0 f'(x)=6x^2-6x-12=0 Taking out roots of this differentiated equation we get x=2 or x= -1. so, for minima at x , f ′ ′ ( x ) = 12 x − 6 > 0 f''(x)=12x-6>0 thus we get x = 2 x=2 this is our local minimum value..

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it is calculus ._.

math man - 6 years, 9 months ago
. .
Mar 14, 2021

f ( x ) = 2 x 3 − 3 x 2 − 12 x + 8 f(x) = 2 x ^ { 3 } - 3x ^ { 2 } - 12x + 8 .

We get x = 2 \text { We get } x = 2 .

Then , 16 − 12 − 14 + 8 = 4 − 14 + 8 = − 10 + 8 = − 2 \text { Then }, 16 - 12 - 14 + 8 = 4 - 14 + 8 = -10 + 8 = -2 .

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