Question

how do I find the use the linearization to approximate the value of f(1.4)?
I know the value of a =1 and f(a) = 1 and the approximation is an underestimate

Answer 1

\[
L(x) -f(a) = f'(a)(x-a)
\]

Answer 2

For me it is relatively easy to remember \[
f'(a) = \frac{L(x)-f(a)}{x-a}
\]

Answer 3

At the very least you could say \[
f'(1)=\frac{L(x)-1}{0.4}
\]

Answer 4

Whoops, should have said: \[
f'(1) = \frac{L(1.4)-1}{0.4}
\]