Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 18

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$f (x) = - 1 + k x + k$ neither touches nor cuts the curve $f (x) = \ln x$ , then minimum value of $k \in$ is

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Important Questions on Monotonicity, Maxima and Minima

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 19

Let

f (x)

be a polynomial with real coefficients which satisfies

f (x) = f^{'} (x) \times f^{'''} (x)

. If

f (x) = 0

satisfies

x = 1, 2, 3

only, then the value of

f^{'} (1) \times f^{'} (2) \times f^{'} (3)

is equal to:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 20

A curve whose concavity is directly proportional to the logarithm of its

x

-coordinates at any of the curve, is given by

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 21

f (x) = 4 t a n x - t a n^{2} x + t a n^{3} x, \forall x \neq n π + \frac{π}{2}, \forall n \in I

, then

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 22

If

f (x) = \{\begin{matrix} 3 + |x - k|, & x \leq k \\ a^{2} - 2 + \frac{s i n (x - k)}{x - k}, & x > k \end{matrix}

has minima at

x = k

, then:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 23

Let

f (x)

be a linear function with properties

f (1) \leq f (2), f (3) \geq f (4)

and

f (5) = 5

, then which of the following is true?

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 24

If $P (x)$ is a polynomial satisfying $P (x^{2}) = x^{2} P (x)$ and $P (0) = - 2, P^{'} (\frac{3}{2}) = 0$ and $P (1) = 0$ . The maximum value of $P (x)$ is

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 25

If the curve

x^{2} = - 4 (y - a)

does not intersect the curve

y = [x^{2} - x + 1]

(where [.] denotes the greatest integer function) in

[0, \frac{1 + \sqrt{5}}{2}]

then

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 26

Analyze the following graph of

f^{'} (x)

:

Question Image

Which is incorrect about

f (x)

for

α < x < β

?