CAT Question Bank  Maxima & Minima

Q8) Find the maximum and minimum values of 3x + 4y if x^2 + y^2 = 14x + 6y + 6 and x, y are positive real numbers.

Q9) f(x) = max (2x + 1, 3  4x). Find minimum value of f(x), if x belongs to [3,7]

Q10) f(x) = minimum (4x + 3, x + 4) for x belongs to 0 to 2. What is the maximum value of f(x)?

Q11) if x * y * z = 2002 and x > y > z ≥ 2 then find the maximum and minimum values of x + y + z

Q12) If (x + 2)^2 = 9 and (y + 3)^2 = 25, then the sum of maximum and minimum values of x/y is ?

Q13) Find the sum of maximum and minimum values of x^2/(1 + x^4) where x is real

Q14) If x + y = 10, then what is the sum of minimum and maximum values of x + y ?

Q15) a, b, c and d are four positive real numbers such that a^2 + b^2 + c^2 + d^2 = 100. What is the maximum
possible value of a + b + c + d ?
(a) 30
(b) 10
(c) 20
(d) None of these

Q16) Find the maximum value of x * y * z, if x^2 + y^3 + z^4 = 26

Q17) If a * b * c * d * e = 32 then minimum value of the expression (a + 1) * (b + 1) * (c + 1) * (d + 1) * (e + 1)

Q18) Find the maximum and minimum value of sin³x + cos³x

Q19) If minimum value of A is 1 then find the minimum value of A + (1/A)

Q20) If f(x) = min(1  3x, 2x  1), find the maximum value of f(x).

Q21) Find the minimum value of (p + q + r)(1/p + 1/q + 1/r) where p, q and r are natural numbers.

Q22) Let x, y, z be three nonnegative integers such that x + y + z = 10. The maximum possible value of xyz + xy + yz + zx is

Q23) which of the following is the maximum value of f(x) = x / (x^2  x + 1) ? ( given x is a real number )
a) 1/3
b) 2
c) 1
d) 1/3

Q24) A function f(x) is defined as f(x) = min{4x + 1, x + 2, 2x + 4}
Then maximum value of f(x) is
a) 2
b) 5/2
c) 8/3
d) 17/6
e) 3

Q25) A function f(x) is defined for all real values of x as min(–x^2, x – 20, –x – 20).
What is the maximum value of f(x)?
(a) –16
(b) –20
(c) –25
(d) None of these

Q26) a + b + c = 0
a^2 + b^2 + c^2 = 1
If a, b, c be real numbers, find the maximum possible value of (9abc)^2

Q27) Find the minimum value of f(x) = (6/x) + x^2