Question 19: The graph of the function y = ax3 + bx2 + cx + d has two extreme points A(0,0), B(1;1), then the coefficients a, b, c, d have values respectively. to be:
\(y’ = 3a{x^2} + 2bx + c\)
We have:
\(\left\{ \begin{array}{l}
y\left( 0 \right) = 0\\
y\left( 1 \right) = 1\\
y’\left( 0 \right) = 0\\
y’\left( 1 \right) = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
d = 0\\
a + b + c + d = 1\\
c = 0\\
3a + 2b + c = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = – 2\\
b = 3\\
c = 0\\
d = 0
\end{array} \right.\)
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