The straight line passing through the origin and point A (1; 3) touches the graph of the function

The straight line passing through the origin and point A (1; 3) touches the graph of the function y = f (x) at the point x0 = 5. Find f ‘(x0).

To begin with, we note that the straight line passing through the origin is a direct proportionality and is given by the formula y = k * x. Substitute the coordinates of the known point:

3 = k * 1;

k = 3;

y = 3 * x – tangent equation.

The slope value is equal to the value of the derivative of the function at the point with the abscissa x0.

3 = y ‘(x0).