IGCSE Additional Math 14.6. Find stationary points Topic Practice

A curve has equation $y=(5-x)(x+2)^{2}$.

Find the x -coordinates of the stationary points on the curve.

Variables x and y are related by the equation $y=x \sqrt{1+2 x}$.

Find the x-coordinate of the stationary point on the curve $y=x \sqrt{1+2 x}$.

（a）Find the x－coordinates of the stationary points on the curve $y=\frac{1}{2}(3-2 x)(x+2)^{2}$ ．［4］
（a）Find the x－coordinates of the stationary points on the curve $y=\frac{1}{2}(3-2 x)(x+2)^{2}$ ．

The function f is defined by $f(x)=3 \sin ^{2} x-2 \cos x$ for $2 \leqslant x \leqslant 4$, where x is in radians.

Find the x-coordinate of the stationary point on the curve y=f(x).

Show that the curve $y=x-\ln \left(x^{2}+2 x\right)$ has exactly one stationary point.
Find the x-coordinate of this point.

The equation of a curve is $y=\frac{\mathrm{e}^{-3 x+2}}{x+1}$ where x<-1.

Hence show that there is only one stationary point on the curve and find its exact coordinates.

The polynomial q(x) is given by $\mathrm{q}(\mathrm{x})=-\frac{1}{3}(2 \mathrm{x}-1)(\mathrm{x}+3)^{2}$.

A curve has equation $y=\left(\frac{x^{2}-1}{x^{2}+1}\right)^{4}$.

Show that the curve has stationary points where x=-1, x=0 and x=1.

The equation of a curve is $\mathrm{y}=\mathrm{kxe}^{-2 \mathrm{x}}$, where k is a constant.

Find the coordinates of the stationary point on the curve $y=10 x e^{-2 x}$.

DO NOT USE A CALCULATOR IN THIS QUESTION.

The polynomial $\mathrm{p}(x)=x^{3}+a x^{2}+b x+c$, where a, b and c are constants, has remainder -5 when divided by x-1. The curve y=p(x) has stationary points at $x=\frac{4}{3}$ and x=2.

Find the values of a, b and c.