Think Logically not mathematically [part-35]

Algebra Level 4

What is the local minimum value of x 3 − 4 x 2 − 3 x + 2 x^3-4x^2-3x+2 ?

-16 Cannot be determined 0

Sudoku Subbu by sudoku subbu , 19, India

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1 solution

Sabhrant Sachan
Jun 26, 2016

f ( x ) = x 3 − 4 x 2 − 3 x + 2 f ′ ( x ) = 3 x 2 − 8 x − 3 ⟹ 3 x 2 − 9 x + x − 3 f ′ ( x ) = ( x − 3 ) ( 3 x + 1 ) Function is increasing for x ∈ ( − ∞ , − 1 3 ) ∪ ( 3 , ∞ ) ⟹ x = 3 is a local minima f ( 3 ) = 27 − 36 − 9 + 2 = − 16 \quad f(x) = x^3-4x^2-3x+2 \\ \quad f^{'}(x) = 3x^2-8x-3 \implies 3x^2-9x+x-3 \\ \quad f^{'}(x) = (x-3)(3x+1)\\ \quad \text{Function is increasing for } x \in \left(-\infty,-\dfrac13\right) \cup (3,\infty) \implies \boxed{x = 3 \text{ is a local minima}} \\ \quad f(3)=27-36-9+2 = \boxed{-16}

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