Applications Of Derivatives Question 142
Question: The tangent drawn at the point (0, 1) on the curve $ y=e^{2x} $ meets x-axis at the point
[RPET 2002]
Options:
A) $ (1/2,,0) $
B) $ (-1/2,0) $
C) (2, 0)
D) $ (0,0) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=e^{2x} $
therefore $ \frac{dy}{dx}=2e^{2x} $
therefore $ ( \frac{dy}{dx} ) _{(0,,1)}^{{}}=2 $
Equation of tangent is, $ y-1=2(x-0)\Rightarrow y=2x+1 $ This tangent meets x-axis,
$ \therefore y=0 $
therefore $ 0=2x+1\Rightarrow x=-1/2 $ \
Co-ordinates of the point $ ( -\frac{1}{2},,0 ). $
BETA
