Short Answer TypeFind the maximum and minimum values, if any, of the following functions without using the derivatives:
– (x – 1)2 + 10
Find the maximum and minimum values, if any, of the following functions without using the derivatives:
(2 x – 1)2 + 3
Find the maximum and minimum values, if any, of the following functions without using the derivatives:
4x2 – 4x + 11
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
x3 + 1
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
| x + 2 |
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
– | x + 1 | + 3
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin (2x + 3)
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin 2x + 5
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
|sin 4x + 3|
Let f(x) = |sin 4x + 3|
∵ – 1 ≤ sin 4x ≤ 1
∴ – 1 + 3 ≤ sin 4x + 3 ≤ 1 + 3
⇒ 2 < sin 4x + 3 ≤ 4 ⇒ 2 ≤ | sin 4x + 3 | ≤ 4
⇒ 2 ≤ f (x) ≤ 4
∴ maximum value of f (x) is 4 and minimum value of f (x) is 2.
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin (sin x)
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