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Monotonically Increasing Functions

x 1 3 5 f...

Question

$x$ $1$ $3$ $5$
$f (x)$ $4$ $k$ $3$
Given that f is a continuous function on the interval $[1, 5]$ and that f takes values shown in the table. The function f will have two zeros in the interval $[1, 5]$ if $k =$

A

- 1

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B

0

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C

1

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D

2

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E

3

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Solution

The correct option is A $- 1$

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Similar questions

Q. The absolute maximum value of a function

f

f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1

on the interval

[1, 5]

Q. Find the absolute maximum and minimum values of a function f given by

f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1 on the interval [1, 5]

Q. Consider the function

f (x) = \frac{x^{3}}{4} - sin π x + 3

f, g : [- 2, 3] \to R

be continuous functions which are twice differentiable on the interval

(- 2, 3)

. Let the values of

f

g

- 2, 0, 1

3

be as given in table

	$x = - 2$	$x = 0$	$x = 1$	$x = 3$
$f (x)$	11	-4	6	16
$g (x)$	1	-2	0	2

In each of the intervals

(- 2, 0), (0, 1)

(1, 3)

(f - 5 g)^{''}

never vanishes. Then the correct statement(s) is/are

f, g : [- 1, 2] \to R

be continuous functions which are twice differentiable on the interval

(- 1, 2) .

Let the values of

f

g

- 1, 0

2

be as given in the following table:

	$x = - 1$	$x = 0$	$x = 2$
$f (x)$	$3$	$6$	$0$
$g (x)$	$0$	$1$	$- 1$

In each of the interval

(- 1, 0)

(0, 2)

(f - 3 g)^{''}

never vanishes. Then the correct statement(s) is(are)

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