I- Maximum value of -5 x 2 -2 x -3 is 17 5 -II- Minimum value of 3x2-7x-9 is 59-6 at x -7-6 - Which of the above statements is-are true -

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Indeterminate Forms

I: Maximum va...

Question

I: Maximum value of $- 5 x^{2} + 2 x + 3$ is $\frac{17}{5}$ .
II: Minimum value of $3 x^{2} - 7 x + 9$ is $\frac{59}{6}$ at $x = - \frac{7}{6}$ .
Which of the above statement(s) is/are true ?

Only I

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Only II

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Both I and II

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Neither I nor ll

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Solution

The correct option is C Neither I nor ll
$y = - 5 x^{2} + 2 x + 3$
$y^{1} = 0$ at x max
$∴$ the value is maximum at that point.
$- 10 x + 2 = 0$
$x = \frac{1}{5}$
$(\frac{1}{5}) = - \frac{1}{25} + 5 + \frac{2}{5} + 3$
$= \frac{10}{5}$
(II) $y = 3 x^{2} - 7 x + 9$
$= 3 (\frac{49}{36}) + \frac{7 \times 7}{6} + 9$
$\frac{49}{12} + \frac{49}{6} + 9$
$= \frac{49 + 98 + 108}{12}$
$= \frac{255}{12}$
$= \frac{85}{4}$
Both the statements are false.

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I.

(3 x + 4 y = 5 and 2 x + 3 y = 9) \Rightarrow (x = - 21 and y = 17)

II.

(x - y + 1 = 0 and 3 x - 5 y + 1 = 0) \Rightarrow (x = - 2 and y = - 1)

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I: Maximum value of −5x2+2x+3 is 175 .II: Minimum value of 3x2−7x+9 is 596 at x=−76 . Which of the above statement(s) is/are true ?

The correct option is C Neither I nor lly=−5x2+2x+3y1=0 at x max∴ the value is maximum at that point.−10x+2=0x=15(15)=−125+5+25+3=105(II) y=3x2−7x+9=3(4936)+7×76+94912+496+9=49+98+10812=25512=854 Both the statements are false.

I: Maximum value of $- 5 x^{2} + 2 x + 3$ is $\frac{17}{5}$ .
II: Minimum value of $3 x^{2} - 7 x + 9$ is $\frac{59}{6}$ at $x = - \frac{7}{6}$ .
Which of the above statement(s) is/are true ?