(i)[3]
If the curve has no stationary point, show that $a^2 < 3b$.
(ii)[3]
For the case $a = -6$ and $b = 9$, find the set of $x$ values for which $y$ is a decreasing function of $x$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is given by $y = x^3 + ax^2 + bx$, with $a$ and $b$ as constants.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $y=x^3+ax^2+bx$ to obtain $\frac{dy}{dx}=3x^2+2ax+b$.” …
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