Find the absolute maximum value of f(x)=4 x-1 2 x^2 in interval [… - Vidyadip

MCQ

Find the absolute maximum value of $f(x)=4 x-\frac{1}{2} x^2$ in interval $\left[-2, \frac{9}{2}\right]$.

✓
8
B
9
C
6
D
10

✓

Answer

Correct option: A.

8

(A)Here $f(x)=4 x-\frac{1}{2} x^2$
$
\therefore \quad f^{\prime}(x)=4-x
$
now $f^{\prime}(x)=0 \Rightarrow 4-x=0 \Rightarrow x=4$
Thus, $\quad f(-2)=4(-2)-\frac{1}{2}(-2)^2=-8-2=-10$
$\begin{aligned}f(4) & =4(4)-\frac{1}{2}(4)^2=16-8=8 \\\text { and } \quad f\left(\frac{9}{2}\right) & =4\left(\frac{9}{2}\right)-\frac{1}{2}\left(\frac{9}{2}\right)^2=18-\frac{81}{8}=\frac{63}{8}\end{aligned}$
Hence absolute maximum value is 8 at $x=4$.

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 Applications of Derivative→Applications of Derivative — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\alpha \in(0, \infty)$ and $A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$. If $\operatorname{det}\left(\operatorname{adj}\left(2 \mathrm{~A}-\mathrm{A}^{\mathrm{T}}\right) \cdot \operatorname{adj}\left(\mathrm{A}-2 \mathrm{~A}^{\mathrm{T}}\right)\right)=2^8$, then $(\operatorname{det}(\mathrm{A}))^2$ is equal to :

If $\vec{a}=(\hat{i}+2 \hat{j}-3 \hat{k})$ and $\vec{b}=(3 \hat{i}-\hat{j}+2 \hat{k})$ then the angle between $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$ is

The function $f : R \rightarrow R$ defined by $f(x) = 2^x + 2^{|x|}$ is:

Consider the system of linear equations

$x+y+z=5, x+2 y+\lambda^2 z=9$

$x+3 y+\lambda z=\mu$, where $\lambda, \mu \in R$. Then, which of the following statement is NOT correct?

Choose the correct answer from the given four options.If two events are independent, then :

If $A = [1\,2\,3],B = \left[ \begin{array}{l}2\\3\\4\end{array} \right]$ and $C = \left[ {\begin{array}{*{20}{c}}1&5\\0&2\end{array}} \right]$, then which of the following is defined

If n = p, then order of matrix 7X - 5Z is:

The function $\text{f(x)}=1+|\cos\text{x}|$ is:

If the integers $m$ and $n$ are chosen at random between $1$ and $100$, then the probability that a number of the form ${7^m} + {7^n}$ is divisible by $5$ equals

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors. Then which one of the following statements is TRUE?