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PLEASE HELP Which expression represents the difference quotient of the function f (x) = negative StartRoot 2 x EndRoot?

PLEASE HELP Which expression represents the difference quotient of the function f x negative StartRoot 2 x EndRoot class=

Respuesta :

Upendo

Answer:

c is the correct option

Step-by-step explanation:

from,

f'(x) = h >0 f(x + h) - f(x)

h

f(x) = - √2x

f(x + h) = - √(2x + h)

f'(x) = h>0 -√(2x + h) - √2x

h

rationalize the denominator

= h>0 -√(2x + h) + √2x (-√(2x + h) - √2x)

h (-√(2x + h) - √2x)

= h>0 4x + 2h - 4x

h(-√(2x + h) -√2x)

= h>0 2h

h(-√(2x+h) - √2x)

= h>0 2

-√(2x+h) - √2x

[tex]\\ \sf\longmapsto f(x)=\sqrt{2x}[/tex]

Now

[tex]\\ \sf\longmapsto \dfrac{1}{-(\sqrt{2x+2h}-\sqrt{2x})}[/tex]

There we plot 2h because if we break root over then it becomes √2h which satisfies f(x)

[tex]\\ \sf\longmapsto \dfrac{1}{-\sqrt{2x+2h}+\sqrt{2x}}[/tex]

Option D

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