Question

find the gradient of the tangent to the graph of ( f ) at the point where ( x = 2 ).

Explanation:

Step1: Select two points on the tangent line

We can choose two points on the tangent line. Let's say \((1,0)\) and \((2,5)\) (by observing the grid - like graph, assuming each small square has a side - length of 1).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 1,y_1 = 0,x_2=2,y_2 = 5\). Then \(m=\frac{5 - 0}{2 - 1}\).

Answer:

\(5\)