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MHT CET20244 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The equation of the tangent to the curve y=1- e ^ x 3 at the point of intersection with Y -axis is

Options

  1. Ax-3 y=0
  2. Bx+3 y=0
  3. Cx+2 y=0
  4. D3 x^ +y=0

Correct answer

B. x+3 y=0

Step-by-step solution

Given equation of curve is y=1- e ^ x 3 ...(i) Since, curve intersects Y-axis, x=0 aligned & y=1- e ^ 0 3 =1-1 & y=0 aligned Tangent to the curve passes through origin Slope of tangent = d y ~d x Differentiating (i) w.r.to x , we get d y ~d x = - e ^ x^3 3 3 ( d y ~d x )_ (0,0) = - e ^ 0 3 3 = -1 3 Equation of tangent is aligned & y-0= -1 3 (x-0) & 3 y=-x & x+3 y=0 aligned

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