Solution:
The values provided in the questions are f(x) = 5x2 - 2 , h ≠ 0. find (f(x+h) - f(x)) / h
let
f(x) = 5x2 - 2 ---------------------------->1
find
(f(x+h) - f(x)) / h ----------------------->2
substitute x = x+h into equation 1
f(x+h) = 5(x+h)2 - 2
f(x+h) = 5(x2 + h2 + 2xh) - 2
f(x+h) = 5x2 + 5h2 +10xh - 2 --------------------->3
substitute equation 1 and 3 into equation 2
= ( ( 5x2 + 5h2 +10xh - 2) - ( 5x2 - 2) ) / h
= ( 5x2 + 5h2 +10xh - 2 - 5x2 + 2 ) / h
= (5h2 +10xh ) / h
= h ( 5h + 10x) / h
= 5h + 10x
= 5( h + 2x)
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