NDA2021MathematicsApplication of DerivativesActual
Where does the tangent to the curve y=e^x at the point (0,1) meet x -axis?
Options
- A(1,0)
- B(-1,0)
- C(2,0)
- D(- 1 2 , 0 )
Correct answer
B. (-1,0)
Step-by-step solution
Curve : y=e^x Slope of tangent = d y d x =e^x ( d y d x )_ (0,1) =e^0=1 Equation of Tangent, aligned & y-y₀= ( d y d x )_ (0,1) (x-x₀ ) & y-1=1 (x-0) & y-1=x & y=x+1 aligned When tangent meet x -axis, y coordinates becomes zero y=x+1 0=x+1 x=-1 Hence, point (-1,0)