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Applications of Derivative Maths - Applications of Derivative

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 31 questions in this chapter.

Question types

Applications of Derivative question types

31 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

31
Questions
5
Question groups
5
Question types
Sample Questions

Applications of Derivative questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
The minimum value of function $f(x)=2 \cos x+x$ in interval $\left[0, \frac{\pi}{2}\right]$ :
  • A
    2
  • B
    $\frac{\pi}{6}+\sqrt{3}$
  • ✓
    $\frac{\pi}{2}$
  • D
    None of these

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Function $f(x)=2 x^3-15 x^2+36 x+6$ is increasing in which of interval :
  • ✓
    $(-\infty, 2) \cup(3, \infty)$
  • B
    $(-\infty, 2)$
  • C
    $(-\infty, 2] \cup[3, \infty)$
  • D
    $[3, \infty)$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
Function $y=x^2 e^{-x}$ is decreasing in which of interval :
  • A
    $(0,2)$
  • B
    $(2, \infty)$
  • C
    $(-\infty, 0)$
  • ✓
    $(-\infty, 0) \cup(2, \infty)$

Answer: D.

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Q 102 Marks2 Marks
The radius of a circle is increasing uniformly at the rate of $3 cm / s$. Find the rate at which the area of the circle is increasing when the radius is 10 cm .
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Q 142 Marks2 Marks
For function $y=f(x)$ if $\frac{d y}{d x}=6(x-2)(x-3)$ then find the value of $x$ for the maximum value of $y$.
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Q 163 Marks3 Marks
A particle is moving in straight line such that on time $t$ distance ( $S$ ) from a fixed point is proportional to $n$ power of time. If at time $t$ its velocity $( V )$ and a acceleration then prove that :$
V^2=\frac{n a S}{(n-1)}
$
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Q 183 Marks3 Marks
In interval $[ 1 , 5]$ Find the absolute maximum and absolute minimum values of given function $f(x)=x^2-4 x+8$.
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Q 193 Marks3 Marks
Radius of a sphere measure 9 cm in which error is 0.02 cm . Find the approximate error in calculation of volume.
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Q 224 Marks4 Marks
In interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$, Find the difference in maximum value and minimum value of function $f(x)=\sin 2 x-x$.
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