Complete the table of values for \(y=\dfrac{x^3}{4}-3x+2\).
Values are given to one decimal place where appropriate.
\(x\)
−4
−3
−2
−1
0
1
2
3
4
\(y\)
−2
4.3
6
4.8
2
−0.8
−2
6
[1]
On the grid, draw the graph of \(y=\dfrac{x^3}{4}-3x+2\) for \(-4\leq x\leq4\).[3]
By drawing a tangent, find the gradient of the curve at \(x=-1\).[1]
The equation \(\dfrac{x^3}{4}-3x=k\) has two solutions.
Use your graph to find the two possible values of \(k\).[2]
By drawing a suitable straight line on the grid, solve the inequality \(x^3-16x-4>0\).[3]
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Answer:(a) \(-0.3\). (b) Smooth cubic through table points. (c) About \(-2.25\). (d) \(k=4\) or \(-4\). (e) Within the drawn domain, about \(-3.9<x<-0.25\); globally also \(x>4.1196\ldots\).