<p>The variables \(x\) and \(y\) are connected by the equation \(y = 3x^2 + \frac{5}{x}\).</p>
<p>Some corresponding values of \(x\) and \(y\) are given in the following table.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 350px;"><colgroup><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(x\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(0.4\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(0.6\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(0.8\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(1\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(1.2\)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(1.4\)</th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(y\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(12.98\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(9.41\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(8.17\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(8\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(8.49\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(p\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the value of \(p\).</span></div></li><li><div class="list-item-paragraph">Using a scale of \(1\) cm to \(0.1\) unit, draw a horizontal \(x\)-axis for&nbsp;\(0 \le x \le 1.6\). Using a scale of \(1\) cm to \(1\) unit, draw a vertical \(y\)-axis for&nbsp;\(0 \le y \le 14\).<br>On your axes, plot the points given in the table and join them with a smooth curve.</div></li><li><div class="list-item-content"><span class="list-item-text">Use your graph to find the least value of \(y\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Use your graph to find two solutions of \(3x^2 + \frac{5}{x} = 9\) in the range \(0 \le x \le 1.6\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">By drawing a tangent, find the gradient of the curve at the point \((0.8, 8.17)\).</span></div></li><li><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">On the same axes, draw the graph of \(y = 2x + 7\) for&nbsp;\(0 \le x \le 1.6\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Write down \(x\)-coordinate of the point where the two graphs intersect.</span></div></li><li><div class="list-item-paragraph">This value of \(x\) is a solution of the equation \(3x^3 + Ax^2 + Bx + C = 0\).<br>Find the value of \(A\), \(B\) and \(C\).</div></li></ol></li></ol>

The variables \(x\) and \(y\) are connected by the equation \(y = 3x^2 + \frac{5}{x}\).

Some corresponding values of \(x\) and \(y\) are given in the following table.

Using a scale of \(1\) cm to \(0.1\) unit, draw a horizontal \(x\)-axis for \(0 \le x \le 1.6\). Using a scale of \(1\) cm to \(1\) unit, draw a vertical \(y\)-axis for \(0 \le y \le 14\).\n\nOn your axes, plot the points given in the table and join them with a smooth curve.

Using a scale of \(1\) cm to \(0.1\) unit, draw a horizontal \(x\)-axis for \(0 \le x \le 1.6\). Using a scale of \(1\) cm to \(1\) unit, draw a vertical \(y\)-axis for \(0 \le y \le 14\).
On your axes, plot the points given in the table and join them with a smooth curve.

Use your graph to find the least value of \(y\).

Use your graph to find two solutions of \(3x^2 + \frac{5}{x} = 9\) in the range \(0 \le x \le 1.6\).

By drawing a tangent, find the gradient of the curve at the point \((0.8, 8.17)\).

On the same axes, draw the graph of \(y = 2x + 7\) for \(0 \le x \le 1.6\).

Write down \(x\)-coordinate of the point where the two graphs intersect.

This value of \(x\) is a solution of the equation \(3x^3 + Ax^2 + Bx + C = 0\).\nFind the value of \(A\), \(B\) and \(C\).

Functions and Graphs - Graphical Solution and Gradient of the Curve at a Point

Question 7846f988