Given Functions

Question

For the given function f(x) and f(a) and f(a+h); then use them to find f(a+h)-f(a)/h

 

f(x)=x²+2

Answer 1

Hi Naomi,

 

All you need to do is replace x by a and a+h in f(x) to find f(a) and f(a+h).

 

f(a) = a^2 + 2

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

= a^2 + 2ah + h^2 + 2

 

f(a+h) - f(a) = a^2 + 2ah + h^2 + 2 - (a^2 + 2)

= h^2 + 2ah

= h(h+2a) 

Then, 

f(a+h)-f(a)/h = h(h+2a) / h

= h + 2a