Maximum value

Algebra Level 3

The greatest value of 2 x 3 − 3 x 2 − 12 x + 1 2x^{3}-3x^{2}-12x+1 , where 2 x 2 − x − 10 ≤ 0 2x^{2}-x-10 \leq 0 is

5 8 7 3

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Shivam Jadhav
Apr 28, 2015

f ′ ( x ) = 0 f'(x)=0 this implies x = − 1 , 2 x=-1,2 f ( − 1 ) = 8 f(-1)=8 f ( 2 ) = − 19 , f ( − 2 ) = − 3 , f ( 5 2 ) = − 33 2 f(2)=-19,f(-2)=-3,f(\frac{5}{2})=\frac{-33}{2} . hence maximum value is 8 .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Yes you're right. You should add in explanation for clarity.

Instead of putting the values ,we can either double differentiate it and check for negative values or we can simply say that since the function was increasing till -1,and starts decreasing after that ,therefore local maxima will exist at -1 (In the second method we need to compare the values at x=-1 and x=5/2)

Abhijeet Verma - 6 years, 1 month ago

Can you add in the explanation?

Anik Mandal - 5 years, 2 months ago

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