Classical

Calculus - Calculus MCQ

6:  

The minimum value of | x2 _ 5x + 21 | is

A.

-5

B.

0

C.

-1

D.

-2

 
 

Option: B

Explanation :

Since value of a mod function cannot be less than zero, therefore
f(x) = | x2 - 5x + 21 | is zero.


7:  

 The value of the improper integral
 
 

A.

1/4

B.

0

C.

-1/4

D.

1

 
 

Option: C

Explanation :


8:  

Value of the definite integral

Calculus objective type questions

A.

-2ln2

B.

2

C.

0

D.

(ln2)2

 
 

Option: D

Explanation :


9:  

The function f(x) = 3x(x - 2) has a

A.

minimum at x = 1

B.

maximum at x = 1

C.

minimum at x = 2

D.

maximum at x = 2

 
 

Option: A

Explanation :

f(x) = 3x (x - 2) = 3x2 - 6x

Differentiating, we get  

 Again diferentiating, 

For maxima or minima, - f '(x) =0

∴  6x-6=0  ⇒ x=1

As f '(x) =6 >0 then f(x) is minimum at x=1
 


10:  

What is the derivative of f(x) =  | x | at x = 0 

A.

1

B.

-1

C.

0

D.

Does not exist

 
 

Option: D

Explanation :

f(x) = |x| and f(x) = x for x > 0 ⇒f(x) = -x for x < 0

Calculus questions

Hence from the graph it is clear that derivative doesn't exists for x=0




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