Bài tập 7 trang 192 SGK Toán 11 NC

Với x₀ ∈ R

Ta có:

\(\begin{array}{*{20}{l}}
\begin{array}{l}
f\prime ({x_0}) = \mathop {\lim }\limits_{x \to {x_0}} \frac{{f(x) - f({x_0})}}{{x - {x_0}}}\\
 = \mathop {\lim }\limits_{x \to {x_0}}  = \frac{{{x_5} - x_0^5}}{{x - {x_0}}}
\end{array}\\
\begin{array}{l}
 = \mathop {\lim }\limits_{x \to {x_0}} ({x^4} + {x^3}{x_0} + {x^2}x_0^2 + xx_0^3 + x_0^4)\\
 = 5x_0^4
\end{array}\\
\begin{array}{l}
f\prime ( - 1) = 5;f\prime ( - 2) = 5.{( - 2)^4} = 80,\\
f\prime (2) = 80
\end{array}
\end{array}\)

-- Mod Toán 11 HỌC247