Download App

6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
If $f(x)=$  $7{e^{{{\sin }^2}x}} - {e^{{{\cos }^2}x}} + 2$, then,$\sqrt {7{f_{\min }} + {f_{\max }}}$ is equal to
  • A
    $0$
  • B
    $\sqrt {10}$
  • C
    $\sqrt {8}$
  • ✓
    $8$
✓

Answer

Correct option: D.
$8$
d
$f(t)=7 t-\frac{e}{t}+2$ for $t \in[1, e],$ where $t=e^{\sin ^{2} x}$

$\Rightarrow f^{\prime}(t)=7+\frac{e}{t^{2}}>0 \forall t \in R$

Hence $f$ is increasing function.

$\therefore f_{\min }=f(1)=7-e+2=9-e$

and $f_{\max }=f(e)=7 e-1+2=7 e+1$

Hence answer is 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 6. Application of derivatives→6. 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

Let us consider a curve, $\mathrm{y}=\mathrm{f}(\mathrm{x})$ passing through the point $(-2,2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x)+x f^{\prime}(x)=x^{2}$ Then :
→
If $\text{xy}-\log_\text{e}\text{y}=1$ satisfies the equation $\text{x}(\text{yy}_2+\text{y}_1^2)-\text{y}_2+\lambda\text{yy}_1=0,$ then $\lambda=$
  1. -3
  2. 1
  3. 3
  4. None of these
→
Let X denote the number of times heads occur in n tosses of a fair coin. If P(X = 4), P(X = 5) and P(X = 6) are in AP, the value of n is:
  1. 7, 14
  2. 10, 14
  3. 12, 7
  4. 14, 12
→
If $y = {\log _{10}}{x^2}$, then ${{dy} \over {dx}}$ is equal to
→
If the matrix AB is zero, then:
  1. It is not necessary that either A = 0 or, B = 0
  2. A = 0 or B = 0
  3. A = 0 and B = 0
  4. All the above statements are wrong
→
The function $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$ is
→
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
→
The value of $12 \int \limits_0^3\left|x^2-3 x+2\right| d x$ is $.............$
→
The area bounded by y = x2 and y = 1 - x2 is:
  1. $\frac{\sqrt{8}}{3}$
  2. $\frac{16}{3}$
  3. $\frac{32}{3}$
  4. $\frac{17}{3}$
→
The function ${x^x}$ is increasing, when
→