The maximum value of fx - 89x2-6x-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 XIII

Mathematics

Range of a 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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Similar questions

Q. Consider f : R + → [−5, ∞ ) given by f ( x ) = 9 x 2 + 6 x − 5. Show that f is invertible with .

Q. Find the intervals in which the following functions are increasing or decreasing.
(i) f(x) = 10 − 6x − 2x²

(ii) f(x) = x² + 2x − 5

(iii) f(x) = 6 − 9x − x²

(iv) f(x) = 2x³ − 12x² + 18x + 15

(v) f(x) = 5 + 36x + 3x² − 2x³

(vi) f(x) = 8 + 36x + 3x² − 2x³

(vii) f(x) = 5x³ − 15x² − 120x + 3

(viii) f(x) = x³ − 6x² − 36x + 2

(ix) f(x) = 2x³ − 15x² + 36x + 1

(x) f(x) = 2x³ + 9x² + 12x + 20

(xi) f(x) = 2x³ − 9x² + 12x − 5

(xii) f(x) = 6 + 12x + 3x² − 2x³

(xiii) f(x) = 2x³ − 24x + 107

(xiv) f(x) = −2x³ − 9x² − 12x + 1

(xv) f(x) = (x − 1) (x − 2)²

(xvi) f(x) = x³ − 12x² + 36x + 17

(xvii) f(x) = 2x³ − 24x + 7

(xviii)

f (x) = \frac{3}{10} x^{4} - \frac{4}{5} x^{3} - 3 x^{2} + \frac{36}{5} x + 11

(xix) f(x) = x⁴ − 4x

(xx)

f (x) = \frac{x^{4}}{4} + \frac{2}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + 7

(xxi) f(x) = x⁴ − 4x³ + 4x² + 15

(xxii) f(x) = 5x³^/2 − 3x⁵^/2, x > 0

(xxiii) f(x) = x⁸ + 6x²

(xxiv) f(x) = x³ − 6x² + 9x + 15

(xxv)

f (x) = {\{x (x - 2)\}}^{2}

Q. The maximum value of

f (x) = \frac{8}{9 x^{2} - 6 x + 5}

in its domain is

Q. The maximum value of

f (x) = \frac{8}{9 x^{2} - 6 x + 5}

in its domain is

Q. Find inverse function of

f (x) = 9 x^{2} + 6 x - 5

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Range of a Quadratic Expression

Standard XIII 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 $f (x) = \frac{8}{4} = 2$