Bài tập 8 trang 192 SGK Toán 11 NC

Bài tập 8 trang 192 SGK Toán 11 NC

a) Đặt f(x) = y= ax²

Với x₀ ∈ R ta có:

\(\begin{array}{*{20}{l}}
{f\prime ({x_0}) = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{f({x_0} + \Delta x) - f({x_0})}}{{\Delta x}}}\\
{ = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{a{{({x_0} + \Delta x)}^2} - ax_0^2}}{{\Delta x}}}\\
{ = \mathop {\lim }\limits_{\Delta x \to 0} a(2{x_0} + \Delta x) = 2a{x_0}}
\end{array}\)

b) Đặt f(x) = y = x³ + 2 

Với x₀ ∈ R ta có:

\(\begin{array}{*{20}{l}}
{f\prime ({x_0}) = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{f({x_0} + \Delta x) - f({x_0})}}{{\Delta x}}}\\
{ = \mathop {\lim }\limits_{\Delta x \to 0} \frac{{{{({x_0} + \Delta x)}^3} + 2 - x_0^3 - 2}}{{\Delta x}}}\\
{ = \mathop {\lim }\limits_{\Delta x \to 0} \left[ {{{({x_0} + \Delta x)}^2} + ({x_0} + \Delta x){x_0} + x_0^2} \right] = 3x_0^2}
\end{array}\)

-- Mod Toán 11