Sample QuestionsApplications of Derivative questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In which of the following intervals is $y=x^2 e^{-x}$ increasing ?
- A
$(1,0)$
- B
$(2,0)$
- C
$(2,-\infty)$
- D
$(0,2)$
View full solution →The minimum value of function $f(x)=2 \cos x+x$ in interval $\left[0, \frac{\pi}{2}\right]$ :
- A
- B
$\frac{\pi}{6}+\sqrt{3}$
- ✓
$\frac{\pi}{2}$
- D
Answer: C.
View full solution →In which of the following, function $f(x)=x^2-4 x$ +6 is increasing :
- A
$(-\infty, 2) \cup(2, \infty)$
- B
$(2, \infty)$
- C
$(-\infty, 2)$
- D
$(-\infty, 2] \cup(2, \infty)$
View full solution →Find the absolute maximum value of $f(x)=4 x-\frac{1}{2} x^2$ in interval $\left[-2, \frac{9}{2}\right]$.
Answer: A.
View full solution →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.
View full solution →Prove that the logarithmic function is increasing on $(0, \infty)$.
View full solution →What different values of $a$ function $f(x)=a x+b$ is decreasing when $x \in R$.
View full solution →Show that function $f(x)=7 x^2-3, x>0$ is increasing function.
View full solution →What do you mean by differential coefficient $\frac{d y}{d x}$ ?
View full solution →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 .
View full solution →Find the maximum and minimum value of function $f(x)=\sin 2 x+5$.
View full solution →Find the interval where function $f(x)=x^3-3 x$ is decreasing.
View full solution →What is the maximum value of $a \sin x+b \cos x$ ?
View full solution →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 $y$.
View full solution →Find the maximum value of $\sin \theta+\cos \theta$.
View full solution →In interval $[ 1 , 5]$ Find the absolute maximum and absolute minimum values of given function $f(x)=x^2-4 x+8$.
View full solution →Radius of a sphere measure $9 \ cm$ in which error is $0.02 \ cm .$ Find the approximate error in calculation of volume.
View full solution →Find the interval for which function $f(x)=x^3-$ $3 x^2-24 x+5$ is increasing.
View full solution →Find the interval for which function $f(x)=2 \log (x-2)-x^2+4 x+1$ is increasing.
View full solution →Prove that function $\sin ^2 x(1+\cos x)$, at $\cos x =\frac{1}{3}$ is maximum.
View full solution →In interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$, Find the difference in maximum value and minimum value of function $f(x)=\sin 2 x-x$.
View full solution →Find the maximum and minimum value of this function. $ f(x)=\sec x+\log \cos ^2 x, 0 < x < 2 \pi$
View full solution →The rate of change of the area of a circle with respect to its radius $r$ at $r=3 cm$ is ________ .
View full solution →If in any circle radius is increasing at the rate of 0.5 $cm / sec$ then rate of increasing circumference is ________ .
View full solution →Maximum value of $f(x)=x e^{-x}$ is _________ .
View full solution →If two real number $x$ and $y$ such that $x>0$ and $x y=1$ then minimum value of $x+y$ is ________ .
View full solution →The minimum value of function $f(x)=x^2+\frac{250}{x}$ is ________ .
View full solution →Find the maximum and minimum value of following function.$2 x^3-15 x^2+36 x+10$
View full solution →Surface area of a spherical bubble is increasing at the rate of $2 cm^2 / sec$. At what rate volume of bubble increasing when radius of bubble is $6 m$ ?
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