WAEC 2010 · Paper 2 · Q3

(a)
Find the equation of the tangent to the curve $y = x^2 - 3x + 4$ at the point where the tangent makes an angle of $135^\circ$ with the positive $x$ -axis.

Worked solution (try it first)

The gradient of the tangent is $\tan 135^\circ = -1$ .
Differentiate: $\dfrac{dy}{dx} = 2x - 3$ .
Set the gradient equal to $-1$ : $2x - 3 = -1$ , so $x = 1$ .
Find $y$ on the curve: $y = 1 - 3 + 4 = 2$ , so the point is $(1, 2)$ .
The tangent: $y - 2 = -1(x - 1)$ .
Rearrange: $x + y - 3 = 0$ .

Report a problem with this question