The maximum value of f x -8-9 x 2-6 x -5 in its domain is

F(x) will be maximum when 9x^2 6x+5 is minimum. nbsp; Let g(x)=9x^2 6x+5, a=9( gt;0) ∴ Minimum value of g(x) 4ac b^24a=180 3636=4 ∴ Maximum value of f(x) ...

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Standard XII

Mathematics

Range of Quadratic Expression

The maximum v...

Question

The maximum value of $f (x) = \frac{8}{9 x^{2} - 6 x + 5}$ in its domain is

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Solution

$f (x)$ will be maximum when $9 x^{2} - 6 x + 5$ is minimum.
Let $g (x) = 9 x^{2} - 6 x + 5, a = 9 (> 0)$
$∴$ Minimum value of $g (x)$
$\frac{4 a c - b^{2}}{4 a} = \frac{180 - 36}{36} = 4$

$∴$ Maximum value of $f (x) = \frac{8}{4} = 2$

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Range of Quadratic Expression

Standard XII Mathematics

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The maximum value of f(x)=89x2−6x+5 in its domain is

f(x) will be maximum when 9x2−6x+5 is minimum. Let g(x)=9x2−6x+5, a=9(>0) ∴ Minimum value of g(x) 4ac−b24a=180−3636=4 ∴ Maximum value of f(x)=84=2

The maximum value of $f (x) = \frac{8}{9 x^{2} - 6 x + 5}$ in its domain is

$f (x)$ will be maximum when $9 x^{2} - 6 x + 5$ is minimum.
Let $g (x) = 9 x^{2} - 6 x + 5, a = 9 (> 0)$
$∴$ Minimum value of $g (x)$
$\frac{4 a c - b^{2}}{4 a} = \frac{180 - 36}{36} = 4$

$∴$ Maximum value of $f (x) = \frac{8}{4} = 2$