Bài tập 2 trang 192 SGK Toán 11 NC

a) Ta có:

f(x) = 2x + 1, cho x₀ = 2 một số gia Δx

\(\begin{array}{*{20}{l}}
{\Delta y = f({x_0} + \Delta x) - f({x_0})}\\
{ = f(2 + \Delta x) - f(2)}\\
{ = 2(2 + \Delta x) + 1 - 5 = 2\Delta x}\\
{ \Rightarrow \frac{{\Delta y}}{{\Delta x}} = 2 \Rightarrow f\prime (2) = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{\Delta y}}{{\Delta x}} = 2}
\end{array}\)

b)

\(\begin{array}{l}
\Delta y = f({x_0} + \Delta x) - f({x_0})\\
 = f(1 + \Delta x) - f(1)\\
 = {(1 + \Delta x)^2} + 3(1 + \Delta x) - 4\\
 = 5\Delta x + {\Delta ^2}x\\
 \Rightarrow \frac{{\Delta y}}{{\Delta x}} = 5 + \Delta x \Rightarrow \mathop {\lim}\limits_{x \to 0} \frac{{\Delta y}}{{\Delta x}} = 5
\end{array}\)

Vậy f'(1) = 5

-- Mod Toán 11 HỌC247