Question

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

Answer 1

`\\ \sf\longmapsto f(x)=√(2x)`

Now

`\\ \sf\longmapsto (1)/(-(√(2x+2h)-√(2x)))`

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

`\\ \sf\longmapsto (1)/(-√(2x+2h)+√(2x))`

Option D

Answer 2

c is the correct option

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