Classical

Calculus - Calculus MCQ

16:  

 If x + y = k, x > 0, y > 0, then xy is maximum when

A.

x = ky

B.

kx = y

C.

x = y

D.

None of these

 
 

Option: C

Explanation :


17:  

Which of the following is correct ?

A.

f(a) is an extreme value of f(x) if f '(a)=0

B.

If f(a) is an extreme value of f(x), then f '(a) = 0

C.

If f '(a) = 0, then f (a) is an extreme value of f(x)

D.

all of these

 
 

Option: D

Explanation :


18:  

Let f(x) = lxl, then

A.

f'(0) = 0

B.

f(x) is maximum at x = 0

C.

f(x) is minimum at x = 0

D.

None of these

 
 

Option: D

Explanation :


19:  

The maxima and minima of the function
f(x) = 2x3 - 15x2 + 36x + 10 occur respectively at

A.

x= 3 and x = 2

B.

x = 1 and x = 3

C.

x = 2 and x = 3

D.

x = 3 and x = 4

 
 

Option: C

Explanation :

f(x)=2x3-15x2+36x+10
f '(x)=6x2-30x+36 and f ''(x)=12x-30
For maxima and minima,
f '(x)=0 
6x2-30x+36 = 0 or
x2- 5x + 6 = 0 or 
X = 3,2

Putting these values of x in equation (ii), we get
f '(3) = 36 - 30 = + 6 positive
Hence minimum value = 3
f ' (2) = 24 - 30 = - 6 negative, hence maximum value = 2


20:  

Limit of the following series as x approaches π/2 is
Calculus mcq

A.

2π/3

B.

π/2

C.

π/3

D.

1

 
 

Option: D

Explanation :

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