Help!
Using the limit definition of the derivative, find f'(2) if f(x)= sqrt (x+2)
+128731 [sqrt ( x + h + 2) - sqrt( x + 2)] / h = multiply top/bottom by [ sqrt(x + h + 2) - sqrt ( x + 2)]
[sqrt ( x + h + 2) - sqrt (x + 2)] [ sqrt( x + h + 2) + sqrt(x + 2)] / ( h * [sqrt(x + h + 2) + sqrt (x + 2) ] )
[ (x + h + 2) - ( x + 2)] / ( h * [sqrt ( x + h + 2) + sqrt(x + 2)] )
h / ( h * [sqrt ( x + h + 2) + sqrt(x + 2)] )
1 / [ sqrt ( x + h + 2) + sqrt (x + 2) ] let h → 0
1 [ sqrt ( x + 2) + sqrt(x + 2) ] =
1 / [ 2 sqrt (x + 2)]
And f ' (2) =
1/ [2 sqrt (2 + 2)] =
1 [ 2 sqrt (4) ] =
1/ [2 * 2] =
1/4
