If #f(x)=x^2+2x+7#, find #(f(a+h)-f(a))/h#?

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Answer 1 · 2017-12-05T15:31:47

#(f(a+h)-f(a))/h=2a+2#

As #f(x)=x^2+2x+7#,

#f(a)=a^2+2a+7# and

#f(a+h)=(a+h)^2+2(a+h)+7#

= #a^2+h^2+2ah+2a+2h+7#

Hence #(f(a+h)-f(a))/h=(a^2+h^2+2ah+2a+2h+7-a^2-2a-7)/h#

= #(h^2+2ah+2h)/h#

= #h+2a+2#

and as #h=0#, #(f(a+h)-f(a))/h=2a+2#