Test Index

UPSC NDA Math Model Paper 6

Comprehension:(Que No. 65 - 66)

Consider the curve

y = e^{2x}

Question : 65 of 120

Marks: +1, -0

Where does the tangent to the curve at (0, 1) meet the x-axis?

Solution:

We have already calculated the slope of tangent at

(0,1)

, which is

2.

Equation of a line passing through a point

(x_1, y_1)

and having slope

m

, is given as,

(y-y_1)=m(x-x_1)

Here, point is

(0,1)

and slope is 2 . So,

\Rightarrow(y-1)=2(x-0)

\Rightarrow y=2x+1

Equation of tangent is given as

y=2x+1

y=0

0=2x+1

\Rightarrow x=\frac{-1}{2}

Hence, tangent meets

x

-axis at

\left(-\frac{1}{2},0\right)

Go to Question:

Prev Question

Next Question