Min value

Algebra Level 3

Find the minimum value of

4 x 2 − 6 x + 1 4x^2-6x+1

where x x ranges across all real numbers.


The answer is -1.25.

Parth Lohomi by Parth Lohomi , 20, India

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1 solution

Shaurya Chats
Jul 21, 2014

Two methods... either write 4 x 2 − 6 x + 1 4x^{2}-6x+1 as ( 2 x − 3 2 ) 2 − 5 4 {(2x-\frac{3}{2})}^{2} - \frac{5}{4} , minimise the square part to get − 5 4 \boxed{-\frac{5}{4}} , or differentiate the function, equate it to zero and put the value of x x in it to get − 5 4 \boxed{-\frac{5}{4}} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The first method is the best solution to solve this problem!

Dang Anh Tu - 6 years, 10 months ago

There's also the way of finding the vertex, i.e. x v = − b 2 a x_v=-\frac{b}{2a} , and plugging it in to get the minimum value.

mathh mathh - 6 years, 10 months ago

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