CAIE IGCSE Mathematics Gradients and Stationary Points

Review CAIE IGCSE Mathematics gradients and stationary points through dy/dx=0, turning-point coordinates, tangent equations and gradient conditions.

Exam points

set dy/dx=0 and solve for turning-point x-values before finding coordinates
use a derivative at a given x-value to calculate curve gradients or tangent equations
apply gradient conditions such as a tangent gradient of 10 or zero to locate points

[Maximum number: 2]

$y=3 x^{2}-12 x+7$

Find the coordinates of the point on the graph of $y=3x^2-12x+7$ where the gradient is 0.
$(\qquad,\qquad)$

(2,-5)
B1 for each
If 0 scored, M1 for their $6x-12=0$ or states $\frac{dy}{dx}=0$

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