Mathematics MCQ - Calculus

26 The minimum value of | x²-5x+21 | is

A
-5
B
0
C
-1
D
-2

View Explanation
Comment

Since the value of a mod function cannot be less than zero, therefore f(x) = | x²-5x+2 | is zero.

27 Sum of the perimeters of a circle and a square is 1. If sum of the area is least, then

A
side of the square is double the radius of circle
B
side of the square is 1/2 of the radius of the circle
C
side of the square is equal to radius of the circle
D
none of these

View Explanation
Comment

28 The maximum slope of the curve

-x³ + 6x² + 2x + 1 is

A
14
B
16
C
19
D
-13

View Explanation
Comment

Let f(x) = -x³ + 6x² + 2x + 1

Slope of the function is, f'(x) = -3x² + 12x + 2 = F(x) (say) Now to find minimum or maximum of F(x) Therefore F'(x) = - 6x + 12 F"(2) = -6 For maxima and minima, F'(x) = 0 ⇒ x = 2

Therefore F"(2) = -6

Hence F(x) (slope) is maximum at x = 2

Maximum slope = F(2) = -3(2)2 + 12(2) + 2 = 14

29 Directional derivative of f ( x, y, z ) = x² + y² + z² at the point (1, 1, 1) in the direction i - k is

A
0
B
1
C
√2
D
2√2

View Explanation
Comment

30 The function f(x) = x³ - 6x² + 3x + 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

View Explanation
Comment

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

Mathematics MCQ - Calculus

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