The correct option is C 16
Given, equation of curve is y=x2−x+4
Slope of tangent P(1,4) is
(dydx)=2x−1
⇒(dydx)(1,4)=2−1=1
Equation of tangent is
y−4=1(x−1)
⇒y−x=3 ....(i)
and equation of normal at point P(1,4) is
y−4=−1(x−1)
⇒x+y=5 ....(ii)
Since, the tangent cuts x-axis at A
Therefore, coordinates of A are (−3,0) and the normal cuts x-axis at B and coordinates of B are (5,0).
Therefore, area of ΔPAB
=12∣∣
∣∣141−301501∣∣
∣∣
=12|[−4(−3−5)]|
=12|32|
=16 sq units