Applications of derivatives Previous Year Questions (PYQs) for CMI BS Hons: 4+ Solved Questions with Step-by-Step Solutions

Solve 4+ Applications of derivatives previous year questions for CMI BS Hons with answers and detailed solutions. Free sample questions below.

Applications of derivatives: Solved Questions with Step-by-Step Explanations (4 Problems)

Question 1 MSQ

Let $x$ be a variable that takes real values, and let $f (x) = x^{3} - 3 x$ . Which of the following statements is/are true?

A.
$f (x)$ has a local maximum at $x = - 3$
B.
$f (x)$ has a local maximum at $x = - 1$
C.
$f (x)$ has a local minimum at $x = 3$
D.
$f (x)$ has a global minimum at $x = 1$

Question 2 MSQ

Let $f (x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_{0}$ in the domain is called an inflection point of $f (x)$ if the second derivative $f^{''} (x)$ changes sign at $x_{0}$ . Given the function $f (x) = \frac{x ^{5}}{20} - \frac{x ^{4}}{2} + 3 x + 1$ , which of the following statements are true?

A.
$x_{0} = 0$ is not an inflection point.
B.
$x_{0} = 6$ is the only inflection point.
C.
$x_{0} = 0$ and $x_{0} = 6$ , both are inflection points.
D.
The function does not have an inflection point.

Question 3 MSQ

Let $f$ be a single variable, real valued function such that all its derivatives exist. We say that $f$ changes sign at some point $x_{0}$ in the domain if the product $f (x_{0} + ϵ) \cdot f (x_{0} - ϵ) < 0$ for small enough, positive $ϵ$ .

A.
If $x_{0}$ is a flex point of $f$ then $f^{''} (x_{0}) = 0$ .
B.
If $f^{'} (x_{0}) = 0$ then $x_{0}$ is a turning point of $f$ .
C.
If $f^{''} (x_{0}) = 0$ then $x_{0}$ is a flex point of $f$ .
D.
If $x_{0}$ is a flex point of $f$ then $f^{'} (x_{0}) \neq = 0$ .

Question 4 MSQ

A spherical ball of ice of radius $20 m$ is dropped in a vat of hot water. The ice melts in such a way that (i) the shape of the ball remains spherical, and (ii) the radius of the ball decreases at a constant rate of $0.5 m s^{- 1}$ . At what rate does the volume of the ice ball decrease, when the radius of the ball is $15 m$ ?

A.
$100 π m^{3} s^{- 1}$
B.
$225 π m^{3} s^{- 1}$
C.
$450 π m^{3} s^{- 1}$
D.
$600 π m^{3} s^{- 1}$

Applications of derivatives Previous Year Questions (PYQs) for CMI BS Hons: 4+ Solved Questions with Step-by-Step Solutions

Applications of derivatives: Solved Questions with Step-by-Step Explanations (4 Problems)

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