Q5. The function f(x) = 2x2 - 8x + 4 is increasing on the interval (A) [2,0) (B) (1,0) (C) [2,00) (D) [2,4)
Answers
Correct Question:
The function f(x) = 2x2 - 8x + 4 is increasing on the interval (A) [2,0) (B) (1,0) (C) [2,∞) (D) [2,4)
Given :
f(x) = 2x² - 8x + 4
Or
y = 2x² - 8x + 4
Let's differentiate w. r. t. x
- Let's find out critical point
- ∞ ______________________ ∞
Let's check in which interval it's increasing
- Put any value less than 2 in 4x - 8
- x = 0
→ 4 × 0 - 8 = - 8
So, it is decreasing at (-∞, 2] for any value less than 2
- Put any value more than 2 in 4x - 8
- x = 3
→ 4 × 3 - 8 = 12 - 8 = 4
So, it is increasing at [2, ∞) for any value more than 2
Hence, correct option is C
Question
The function f(x) = 2x2 - 8x + 4 is increasing on the interval (A) [2,0) (B) (1,0) (C) [2,00) (D) [2,4)
Answer
= f(x)=2x²-8x+4
Let's different between w.r.t.x
dy/dx = 2 dx²/dx -8 dx/dx +4
dy/dx=4x-8
So,
= dy/dx = 0
= 4x-8 = 0
x= 8/4=2
Now the interval increasing
Let put a value less than 2 in 4x-8
• x=0
• 4×0-8=-8
Put any value more than 2 in 4x -8
• x=3
= 4×3-8 = 12-8=4
So, it increasing at [2,∞] for any value more than 2