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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

Where does the tangent to the curve y=e^x at the point (0,1) meet x...

Where does the tangent to the curve y=exy=e^x at the point (0,1)(0,1) meet xx-axis?

Options

  1. A(1,0)(1,0)
  2. B(−1,0)(-1,0)
  3. C(2,0)(2,0)
  4. D(−12,0)\left(-\frac{1}{2}, 0\right)

Correct answer

B. (−1,0)(-1,0)

Step-by-step solution

Curve : y=exy=e^x Slope of tangent =dydx=ex(dydx)(0,1)=e0=1→=\frac{d y}{d x}=e^x\left(\frac{d y}{d x}\right)_{(0,1)}=e^0=1\rightarrow Equation of Tangent, y−y0=(dydx)(0,1)(x−x0)y−1=1×(x−0)y−1=xy=x+1\begin{aligned} & y-y_0=\left(\frac{d y}{d x}\right)_{(0,1)}\left(x-x_0\right) \\ & y-1=1 \times(x-0) \\ & y-1=x \\ & y=x+1 \end{aligned}\rightarrowWhentangentmeetWhen tangent meetx−axis,-axis,ycoordinatesbecomeszerocoordinates becomes zero\therefore y=x+1 \Rightarrow 0=x+1 \Rightarrow x=-1Hence,pointHence, point(-1,0)$
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