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Maxima and Minima
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
- A
One, at π/2
- B
One, at 3π/2
- C
Two, at π/2 and 3π/2
- D
Two, at π/4 and 3π/2
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
- A
0
- B
1
- C
2
- D
3
Question 3
What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the interval [0, 2]?
- A
6
- B
10
- C
12
- D
5.5
Question 4
If x = -1 and x = 2 are extreme points of f(x) = α log |x| + β x2 + x then
- A
α = -6, β = -1/2
- B
α = 2, β = -1/2
- C
α = 2, β = 1/2
- D
α = -6, β =1/2
Question 5
What is the least value of the function f(x) = 2x2- 8x - 3 in the interval [ 0 , 5] ?
- A
-15
- B
7
- C
-11
- D
-3
Question 6
The value of x at which y is minimum for y = x2 − 3x + 1 is
- A
-3/2
- B
3/2
- C
0
- D
-5/4
Question 7
The expression [ (x + y) + |x – y| ] / 2 is equal to __________ .
- A
the maximum of x and y
- B
the minimum of x and y
- C
1
- D
none of the above
Question 8
The function f(x) = ax + (b/x), (a > 0, b > 0, x > 0) has the least value at x = ______.
- A
√(a/b)
- B
√(b/a)
- C
√(ab)
- D
(a+b)/2
Question 9
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
- A
0
- B
1
- C
2
- D
3
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:
- A
0, -1
- B
-1, 0
- C
0, 1
- D
-1, 2
There are 10 questions to complete.