If the function f(x) = x^2 - kx + 5 is increasing on [2, 4], then… - Vidyadip

MCQ

If the function $f(x) = x^2 - kx + 5$ is increasing on $[2, 4]$, then:

A
$\text{k}\in(2,\infty)$
B
$\text{k}\in(-\infty,2)$
C
$\text{k}\in(4,\infty)$
✓
$\text{k}\in(-\infty,4)$

✓

Answer

Correct option: D.

$\text{k}\in(-\infty,4)$

$f(x) = x^2 - kx + 5$
$f\ '(x) = 2x - k$
Given$:\ f(x)$ is increasing on $[2, 4].$
$\Rightarrow f\ '(x) > 0$
$\Rightarrow 2x - k > 0$
$\Rightarrow k < 2x$
$\because\ \text{x}\in[2,4],$ maximum value of $k$ is $4, k < 4.$
$\therefore\ \text{k}\in(-\infty,4)$

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 APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer from the given four options.Corner points of the feasible region determined by the system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0).$ Let $Z = px + qy,$ where $p, q > 0.$ Condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3, 0)$ and $(1, 1)$ is:

At what point the slope of the tangent to the curve $x^2 + y^2 - 2x - 3 = 0$ is zero :

The area enclosed by $y ^{2}=8 x$ and $y=\sqrt{2} x$ that lies outside the triangle formed by $y=\sqrt{2} x, x=$ $1, y=2 \sqrt{2}$, is equal to

The number which exceeds its square by the greatest possible quantity is,

Degree of the differential equation $\sin x+\cos \left(\frac{d y}{d x}\right)=y^2$ is

If A and B are such that $\text{P}(\text{A}\cup\text{B})=\frac{5}{9}$ and $\text{P}(\overline{\text{A}}\cup\overline{\text{B}})=\frac{2}{3},$ then $\text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=$

The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ is

Choose the correct answer from the given four options.The order and degree of the differential equation $\Big[1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big]=\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}$ are:

The solution of the equation $(1 + {x^2})\frac{{dy}}{{dx}} = 1$ is

The number of discontinuous functions $y(x)$ on $[-2,2]$ satisfying $x^2+y^2=4$ is