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

More "M.C.Q (1 Marks)" from STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when:

Namita walks $14$ metres towards west, then turns to her right and walks $14$ metres and then turns to her left and walks $10$ metres. Again turning to her left she walks $14$ metres.What is the shortest distance $($in metres$)$ between her starting point and the present position?

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations

$x+y+z=5$ ; $x+2 y+3 z=\mu$ ; $x+3 y+\lambda z=1$

is constructed. If $\mathrm{p}$ is the probability that the system has a unique solution and $\mathrm{q}$ is the probability that the system has no solution, then :

Choose the correct answer from the given four options : The area of the region bounded by the circle $x^2 + y^2 = 1$ is :

Let $f(x) = \frac{{1 - \tan x}}{{4x - \pi }},\;x \ne \frac{\pi }{4},\;\;x \in \left[ {0,\frac{\pi }{2}} \right]$, If $f(x)$ is continuous in $\left[ {0,\frac{\pi }{2}} \right]$, then $f\left( {\frac{\pi }{4}} \right)$ is

The area of the region bounded by the curve $\text{y}=\sqrt{16-\text{x}^2}$ and $x-$ axis is :

Subtraction of integers is:

If $f(x) = A\sin \left( {\frac{{\pi x}}{2}} \right) + B,$ $f'\left( {\frac{1}{2}} \right) = \sqrt 2 $ and $\int_0^1 {f(x)\,dx = \frac{{2A}}{\pi },} $ then the constants $A$ and $B$ are respectively

Let $f(x) = \sin x$ and $g(x) = \ln |x|$. If the ranges of the composite functions $fog$ and $gof$ are ${R_1}$ and ${R_2}$ respectively, then

If a line makes angle $\alpha,\beta$ and $\gamma$ with the axes respectively, then $\cos2\alpha+\cos2\beta+\cos2\gamma=$