Applications Of Derivatives Question 57
Question: If the length of sub-normal is equal to the length of sub-tangent at my point (3, 4) on the curve y=f(x) and the tangent at (3, 4) to y=f(x) meets the coordinate axes at A and B, then the maximum area of the triangle OAB, where O is origin, is
Options:
A) 45/2
B) 49/2
C) 25/2
D) 81/2
Show Answer
Answer:
Correct Answer: B
Solution:
Length of sub-normal = length of the sub-tangent or $ \frac{dy}{dx}=\pm 1 $ If $ \frac{dy}{dx}=1 $ , equation of the tangent is $ y-4=x-3 $ or $ y-x=1 $ area of $ \Delta OAB=\frac{1}{2}\times 1\times 1=\frac{1}{2} $ If $ \frac{dy}{dx}=-1, $ equation of the tangent is $ y-4=-x+3 $ or $ y+x=7, $ Area $ =\frac{1}{2}\times 1\times 1=\frac{1}{2} $
BETA
