SOLUTION: If f(x)=x squared+5, find f(a+h)-f(a)

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Question 90262This question is from textbook
: If f(x)=x squared+5, find f(a+h)-f(a) This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First evaluate f(a+h)


f%28a%2Bh%29=%28a%2Bh%29%5E2%2B5 plug in x=a+h

%28a%2Bh%29%5E2%2B5=a%5E2%2Bha%2Bha%2Bh%5E2%2B5 Foil

%28a%2Bh%29%5E2%2B5=a%5E2%2B2ha%2Bh%5E2%2B5 Combine like terms


So f%28a%2Bh%29=a%5E2%2B2ha%2Bh%5E2%2B5

Now evaluate f(a)

f%28a%29=a%5E2%2B5 plug in x=a

So f%28a%29=a%5E2%2B5

Now combine the two expressions


f%28a%2Bh%29-f%28a%29=%28a%5E2%2B2ha%2Bh%5E2%2B5%29-%28a%5E2%2B5%29 Plug in the expressions previously solved for

f%28a%2Bh%29-f%28a%29=a%5E2%2B2ha%2Bh%5E2%2B5-a%5E2-5 Distribute the negative

f%28a%2Bh%29-f%28a%29=2ha%2Bh%5E2 Combine like terms