Question

Help !!!
See question in image.
Please show workings .
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Answer 1

see explanation

Explanation:

Given f(x) then the derivative f'(x) is

f'(x) = lim(h tends to 0 )
`(f(x+h)-f(x))/(h)`

= lim ( h to 0 )
`(4(x+h)^2-2-(4x^2-2))/(h)`

= lim ( h to 0 )
`(4(x+h)^2-2-4x^2+2)/(h)`

= lim( h to 0 )
`(4x^2+8hx+4h^2-4x^2)/(h)`

= lim( h to 0 )
`(8hx+4h^2)/(h)`

= lim ( h to 0 )
`(4h(2x+h))/(h)` ← cancel h on numerator/ denominator

= lim ( h to 0 ) 4(2x + h) ← let h go to zero

f'(x) = 8x