Answer 1. f(x)= 4x^2
f(5+h)= 4(5+h)^2= 4(25+h^2+10h)= 100+4h^2+40h
f(5)= 4(5)^2= 4*25=100
f(5+h)-f(5)= 100+40h+4h^2-100=40h+4h^4= h(40+4h)
40+4h=(f(5+h)-f(5))/h
Hence proved.
lim x→0 (f(5+h)-f(5)/h)= 40+4h=40+4*0=40
So,
f'(5)= 40
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