Khoảng cách giữa hai điểm cực trị của đồ thị hàm số \(y=(x-2)^{2}(x+1)\) là
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Phương pháp giải
- Tìm hai điểm cực trị.
- Áp dụng công thức khoảng cách giữa hai điểm \(A\left(x_{A} ; y_{A}\right) ; B\left(x_{B} ; y_{B}\right)\) :
\(A B=\sqrt{\left(x_{A}-x_{B}\right)^{2}+\left(y_{A}-y_{B}\right)^{2}}\)
Tìm cực trị của hàm số.
Lời giải
\(f^{\prime}(x)=2(x-2)(x+1)+(x-2)^{2}=2 x^{2}-2 x-4+x^{2}-4 x+4=3 x^{2}-6 x\)
\(f^{\prime}(x)=0 \Leftrightarrow\left[\begin{array}{l}x=0 \Rightarrow y=4 x=2 \Rightarrow y=0\end{array}\right.\)
\(\Rightarrow\) Khoảng cách giữa hai điểm cực trị là \(\sqrt{(0-2)^{2}+(4-0)^{2}}=2 \sqrt{5}\).
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