Question

linear and quadratic approximations formula

let (f(x)) be a function differentiable at (c), and let (m_0 = f(c)) and (m_1 = f(c)).

typesetting: enter \m_0\ and \m_1\ to typeset (m_0) and (m_1).

state the formula of the linear approximation (l(x)) of (f(x)) at (c) in terms of (m_0, m_1, x, c).

(l(x) =)

Explanation:

Recall the standard linear approximation formula

$$ L(x) = f(c) + f'(c)(x - c) $$

Substitute the given parameters

$$
LATEXBLOCK0
$$

Write the final expression

$$ L(x) = m_0 + m_1(x - c) $$

Answer:

State the formula of the linear approximation \(L(x)\) of \(f(x)\) at \(c\) in terms of \(m_0, m_1, x, c\).

\(L(x) =\) <blank>\(m_0 + m_1(x - c)\)</blank>