Question

Determine the area of the triangle formed by the tangent to the graph of the function y = 3 – x² drawn at the point (1, 2) and the coordinate axes.

Answer 1

y = 3 – x²

= slope of the tangent at (1, 2) 

∴ equation of the tangent at (1, 2) is

y – 2= -2(x – 1) 

⇒ y – 2= -2x + 2 

⇒ 2x + y = 4

Let this tangent cuts the coordinate axes at A(a, 0) and B(0, b). 

∴ 2a + 0 = 4 and 2(0) + b = 4 

∴ a = 2 and b = 4

∴ area of required triangle = 1/2 × l(OA) × l(OB)