E-DE04 · Chords, a limit and an intercept triangle
On \(y=2x^2-3x\), P has x-coordinate 2 and Q has x-coordinate \(2+h\), where \(h\ne0\).
Show that the gradient of PQ is \(5+2h\).
Find the chord gradients for \(h=0.1\) and \(h=-0.1\). Hence state the tangent gradient at P as h tends to zero.
Find the tangent equation at P and the area of the triangle it forms with the coordinate axes.
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