An ideal calculus problem

Calculus Level 5

If the function

f ( x ) = 2 x 3 − ( 8 − a ) x 2 + ( a 2 + 19 6 ) x − 12 \large{f(x)=2x^{3}-(8-a)x^{2}+(a^{2}+\frac{19}{6})x-12}

has a local minima at some x ∈ R − x\in R^{-} then value of a a where a ∈ R a\in R

None ( 2 , 3 ) (2,3) ( − 1 , 1 ) (-1,1) ϕ \phi ( − 5 , 9 5 ) (-5,\frac{9}{5})

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Rahul Saxena
Oct 4, 2015

1 Helpful 0 Interesting 0 Brilliant 1 Confused

in question it is given that minima exists means D>0 for quadratic equation by this condition we get[ 5a^2+16a-45>0] by this first option is correct please explain..

Akshay Sharma - 5 years, 6 months ago

Should be option 1

Prithwish Mukherjee - 2 years, 4 months ago

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