Maxima and Minima

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Question 1

Consider the function f(x) = sin(x) in the interval [π/4, 7π/4]. The number and location(s) of the local minima of this function are

  • One, at π/2

  • One, at 3π/2

  • Two, at π/2 and 3π/2

  • Two, at π/4 and 3π/2

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Question 2

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x4 - 16x3 + 24x2 + 37

  • 0

  • 1

  • 2

  • 3

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Question 3

What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the interval [0, 2]?

  • 6

  • 10

  • 12

  • 5.5

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Question 4

If x = -1 and x = 2 are extreme points of f(x) = α log |x| + β x2 + x then

  • α = -6, β = -1/2

  • α = 2, β = -1/2

  • α = 2, β = 1/2

  • α = -6, β =1/2

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Question 5

What is the least value of the function f(x) = 2x2- 8x - 3 in the interval [ 0 , 5] ?

  • -15

  • 7

  • -11

  • -3

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Question 6

The value of x at which y is minimum for y = x2 − 3x + 1 is

  • -3/2

  • 3/2

  • 0

  • -5/4

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Question 7

The expression [ (x + y) + |x – y| ] / 2 is equal to __________ .

  • the maximum of x and y

  • the minimum of x and y

  • 1

  • none of the above

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Question 8

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x4 - 16x3 + 24x2 + 37 is

  • 0

  • 1

  • 2

  • 3

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Question 9

The function f(x) = ax + (b/x), (a > 0, b > 0, x > 0) has the least value at x = ______. 

  • √(a/b)

  • √(b/a)

  • √(ab)

  • (a+b)/2

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Question 10

Consider a function f(x) = 1 - |x| on -1 ≤ x ≤ 1. The value of x at which the function attains a maximum, and the maximum value of the function are:

  • 0, -1

  • -1, 0

  • 0, 1

  • -1, 2

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