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__Few points to remember:__

- sinθ and cosθ both have “1” as their maximum value and “-1” as their minimum value. Hence the values of sinx, sin2x, cosx, cos3x, etc. lie between -1 and 1.
- For sin
^{2}x and cos^{2}x- Minimum value = 0
- Maximum value = 1

- For sinxcosx
- Minimum value = -1/2
- Maximum value = 1/2

- Minimum value of (sin θ cos θ)n = (-1/2)n

Some SSC CGL questions :

**1) What is the least value of 2sin**^{2}θ + 3cos^{2}θ

** (A) 1 (B) 2 (C) 3 (D) 0**

Since 2 is less than 3

Minimum value = 2

** **** Answer: (B)**

** **

** **Hence the least value of 4sec^{2}θ + 9cosec^{2}θ = 13 + 12 = 25

** Answer: (C)**

**4) The maximum of 3sinx – 4cosx is**

** (A) -1 (B) 5 (C) 7 (D) 9**

Maximum value = √(3^2 + 4^2) = √25 = 5

**Answer: (B)**

**Sometimes they ask the minimum/maximum value of a function. In CGL, that function would always be quadratic (ax ^{2} + bx + c). Please note that a quadratic function can’t have both maximum and minimum values. **

**If “a” is positive, then the quadratic function will only have a minimum value. The maximum value would be infinite.****If****“a” is negative, then the quadratic function will only have a maximum value. The minimum value would be infinite.**

But the process to find both minimum and maximum values is same. Hence you shouldn’t be worried about the words “maximum” or “minimum”. When finding the minimum/maximum value of a function, we use the concept of “differentiation”. Although differentiation is a wide topic in itself, but for CGL purpose, we only have to learn the basics.

**Just remember following things:**

- Differentiation of ax
^{n}= a*n*x^{n-1}. Hence differentiation of 4x^{3}= 12x^{2}and differentiation of 3x^{2}= 6x - Differentiation of ax = a. Hence differentiation of 4x is 4.
- Differentiation of any constant is zero. Hence differentiation of 5 is 0.
- If you have to differentiate ax
^{2}+ bx + c, just differentiate each of its term separately and add the result. __Process of finding the minimum value of a function__:- Differentiate the function
- What ever result you get, equate it with zero
- Find the value of x
- Put this value of x in the original function to get the minimum value.

**Let us solve a CGL question:**

**Q. 5) Find the minimum value of (x – 2)(x – 9)
(A) -11/4 (B) 49/4 (C) 0 (D) -49/4 **

(x – 2)(x – 9) = x^2 – 11x + 18

Now we will differentiate (x^2 – 11x + 18)

Note that in this question, the value of a is positive, i.e., +1 and hence the question has asked you the “minimum” value. Had the value of “a” been negative (like -1), they would have asked you the “maximum” value.

Hence, differentiation of (x^2 – 11x + 18) = 2x – 11

Now 2x – 11 = 0

x = 11/2

Put x = 11/2 in (x^2 – 11x + 18) to get the minimum value

Minimum value of x^2 – 11x + 18 = (11/2)^2 – 11*(11/2) + 18 = -49/4

**Answer: (D)**

**If you have any doubt in this article, please drop a comment…
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