Math, asked by sunitkumar17394, 1 day ago

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

Answered by Anonymous
92

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

 \sf \dfrac{dy}{dx} = 2\dfrac{dx^{2} }{dx} - 8\dfrac{dx}{dx} + 4

\sf \dfrac{dy}{dx} = 4x- 8

  • Let's find out critical point

\sf\implies \dfrac{dy}{dx} = 0

\sf\implies 4x - 8 = 0

 \sf\implies 4x = 8

 \sf\therefore x =  \cancel \dfrac{8}{4}  = 2

\qquad - ______________________

\qquad \qquad \qquad \qquad \qquad 2

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

Answered by TheBestWriter
68

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

Option C

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