<p>The gradient of a curve at a point can be obtained by drawing a tangent to the curve at that point and finding the gradient of the tangent.</p>
<p>1. Locate the given point $A$, on the curve.<br></p>
<p style="margin-left: 0.5rem">Place a ruler at the point.</p>
<p>2. Adjust the ruler such that the two angles formed by the ruler and the curve on either side of the point are estimated to be equal.<br></p>
<p style="margin-left: 0.5rem">The ruler should touch the curve at the point only.</p>
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<p>3. Draw a straight line (tangent) through the given point, $A$.</p>
<p>4. Locate $2$ points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ on the tangent (do not choose points that are too close to each other) and write the coordinates of the points on the graph.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765910157618-7zif9wa3p5t.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>5. Calculate the gradient of the tangent at point, $A$ using $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$.</p>
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<p style="text-align: center">This method of finding the gradient of tangent at a point is an <strong>estimation.</strong></p>

The gradient of a curve at a point can be obtained by drawing a tangent to the curve at that point and finding the gradient of the tangent.

1. Locate the given point $A$, on the curve.


2. Adjust the ruler such that the two angles formed by the ruler and the curve on either side of the point are estimated to be equal.


The ruler should touch the curve at the point only.

3. Draw a straight line (tangent) through the given point, $A$.

4. Locate $2$ points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ on the tangent (do not choose points that are too close to each other) and write the coordinates of the points on the graph.

5. Calculate the gradient of the tangent at point, $A$ using $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$.

Essential Steps: Finding the Gradient of the Curve at a Point

Essential Steps: Finding the Gradient of the Curve at a Point