Find Difference Quotient for \(f(x)=x^2\)
Question:
If
$$
f(x)=x^2
$$
find
$$
\frac{f(1.1)-f(1)}{(1.1)-1}
$$
Solution
Given: $$ f(x)=x^2 $$
$$ f(1.1)=(1.1)^2=1.21 $$
$$ f(1)=1^2=1 $$
Therefore, $$ \frac{f(1.1)-f(1)}{(1.1)-1} = \frac{1.21-1}{0.1} $$
$$ = \frac{0.21}{0.1} =2.1 $$
Hence, $$ \boxed{2.1} $$