Classical

Calculus - Calculus MCQ

1:  

If calculus mcq

A.

2x2

B.

√x

C.

0

D.

1

 
 

Option: A

Explanation :

Calculus questions


2:  

The function f(x) = x3 - 6x2 + 9x + 25 has

A.

a maxima at x= 1 and a minima at x = 3

B.

a maxima at x = 3 and a minima at x = 1

C.

no maxima, but a minima at x = 1

D.

a maxima at x = 1, but no minima

 
 

Option: A

Explanation :

f '(x) = 3(x2-4x+3)    f ''(x)=6(x)-12
at  x=1,  f "(1)  
at  x=3, f ''(3) = +ve


3:  

The value of a = is 

A.

>0

B.

2

C.

0 - 1 + 100 - 10 + 1

D.

undefined

 
 

Option: A

Explanation :

Calculus questions answers


4:  

The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is

A.

[-3, 3]

B.

[-2, 2]

C.

[2, 3]

D.

[-1, 1]

 
 

Option: C

Explanation :

Since f(x) = (1/x) is not continuous in [- 3, 3] [- 4, 2] or [- 1, 1], The point of discontinuity is '0'. Only in [2, 3] the function is continuous, and differentiable hence mean value theorem is applicable in [2, 3].


5:  

 If f(x) = | x | , then for interval [-1, 1] ,f(x)

 

 

A.

satisied all the conditions of Rolle's Theorem

B.

satisfied all the conditions of Mean Value Theorem

C.

does not satisied the -conditions of Mean Value Theorem

D.

None of these

 
 

Option: C

Explanation :

Since f(x) = |x| is continuous in [-1, 1] but  it is not differentiable at x = 0 ε (-1, 1)




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