NDA 2018 Maths · Mathematics · Derivatives · medium

If f'(c)=0 and f''(c)<0, then f has a local maximum at x=c. 2. A function continuous on the open interval (0,1) must be bounded on it.

Single correct option

Consider the following statements:
1. If

f'(c)=0

and

f''(c)<0

, then

f

has a local maximum at

x=c

.
2. A function continuous on the open interval

(0,1)

must be bounded on it.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

Statement 1 is the second derivative test and is correct. Statement 2 is false:

f(x)=\frac1x

is continuous on

(0,1)

yet unbounded. Boundedness is guaranteed only on a closed interval

[a,b]

. Hence 1 only.

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