The minimum value of 2 x^2 + x - 1 is - Vidyadip

MCQ

The minimum value of $2{x^2} + x - 1$ is

A
$ - {1 \over 4}$
B
${3 \over 2}$
✓
${{ - 9} \over 8}$
D
${9 \over 4}$

✓

Answer

Correct option: C.

${{ - 9} \over 8}$

c
(c) $f(x) = 2{x^2} + x - 1$

==> $f'(x) = 4x + 1 \Rightarrow f'(x) = 0 \Rightarrow x = - \frac{1}{4}$

$f''\,(x) = 4 = + ve$

$\therefore {[f( - 1/4)]_{\min }} = \frac{2}{{16}} - \frac{1}{4} - 1 = \frac{{ - 9}}{8}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the value of $x,\,y$ and $z$ from the following equation : $\left[\begin{array}{ll}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$

The area enclosed by the closed curve $C$ given by the differential equation $\frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0$ is $4 \pi$.

Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $C$ intersect $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $RS$ is

The sum of $100$ terms of the series $.9 + .09 + .009.........$ will be

From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is

The value of $3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\ldots \infty}}}}$ is equal to

A box contains $15$ green and $10$ yellow balls. lf $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

For the function $ f (x) =$ $\mathop {Lim}\limits_{n \to \infty } \,\,\frac{1}{{1 + n{{\sin }^2}(\pi x)}}$ , which of the following holds ?

If the roots of the equations $p{x^2} + 2qx + r = 0$ and $q{x^2} - 2\sqrt {pr} x + q = 0$ be real, then

If $\sum\limits_{i = 1}^n {i = \frac{{n(n + 1)}}{2}} $, then $\sum\limits_{i = 1}^n {(3i - 2) = } $

Let $M$ denote the median of the following frequency distribution.

Class	$ 0-4$	$ 4-8$	$ 8-12$	$ 12-16$	$ 16-20$
Frequency	$ 3$	$ 9$	$ 10$	$ 8$	$ 6$

Then $20 M$ is equal to :