Question 6

Explanation

To determine the equation of the tangent line, we need to find the gradient ($m$) and the tangent point first.

Determining the Gradient

The gradient is the first derivative of the curve function ($y'$).

Substitute the abscissa $x = 1$ into $y'$ to get the gradient.

Determining the Tangent Point

We find the ordinate value ($y$) when the abscissa $x = 1$.

So, the tangent point is $(1, 2)$.

Determining the Equation of the Tangent Line

Use the formula for the equation of a tangent line $y - y_1 = m(x - x_1)$ with $m = 1$ and point $(1, 2)$.

So, the equation of the tangent line is $y = x + 1$.