Question

greatest value of 4/4x²+4x+9

Answer 1

Answer:

....hope you UNDERSTOOD this answer

Answer 2

The greatest value of this expression is 1/2.

Given,

An expression 4/(4x²+4x+9).

To Find,

The greatest value of this expression.

Solution,

To get the greatest value of 4/(4x²+4x+9), first, we need to find the smallest value of 4x²+4x+9.

So,

4x²+4x+9 = 4(x²+x+9/4)

4x²+4x+9 = 4[(x²+x+1/4)+8/4]

4x²+4x+9 = 4[(x+1/2)²+2]

The value of x+1/2 should be 0, to get the minimum value of 4x²+4x+9

4[(x+1/2)²+2] = 4(2)

Now, the expression becomes

4/(4x²+4x+9) = 4/8 = 1/2

Hence, the greatest value of this expression is 1/2.

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