The following table gives the corresponding values of $x$ and $y$ which are connected by the equ

Question

The following table gives the corresponding values of $x$ and $y$ which are connected by the equation $y={{x}^{3}}-3x-1$.

${x}$	${-1.75}$	${-1.5}$	${-1}$	${-0.5}$	${0}$	${0.5}$	${1}$	${1.5}$	${2}$	${2.25}$
${y}$	${-1.1}$	${0.1}$	${1}$	${0.4}$	${-1}$	${-2.4}$	${-3}$	${a}$	${1}$	${3.6}$

Find the value of $a$, giving your answer correct to 1 decimal place.
Using a scale of $4$ cm to represent $1$ unit on the $x$-axis and $2$ cm to represent $1$ unit on the $y$-axis, draw the graph of $y=x^{3}-3x-1$ in the range $-1.75\le x\le 2.25$.
Use your graph to solve the equation
1. $x^{3}-3x=1$
2. $x^{3}-5x=2$
By drawing a suitable straight line, estimate the gradient of the curve when
1. $\left(-0.5,0.1\right)$,
2. $x=1.5$.

Source correction for (d)(i): at $x=-0.5$, the curve has $y=0.375$, approximately $0.4$, not $0.1$. Draw the tangent at the point on the curve with $x=-0.5$.

Accepted Answer

(a) $-2.1$. (c)(i) $-1.53,-0.35,1.88$; (ii) $-0.41$ on the plotted interval. (d)(i) About $-2.25$; (ii) about $3.75$.

Gradient of a Curve

Gradient of a Curve

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