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AP EAMCET20225 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The line joining the points (0,3) and (5,-2) is a tangent to the curve y= c x+1 , then c=

Options

  1. A1
  2. B-2
  3. C4
  4. D5

Correct answer

C. 4

Step-by-step solution

Slope of line joining the points (0,3) and (5,-2) is 3+2 0-5 =-1 This is equal to the slope of tangent on the curve and that is given by d y d x = -c (x+1)^2 d y d x =-1 c=(x+1)^2 ...(i) Equation of line joining the points (0,3) and (5,2) is given by (y-3)=-1(x-0) . Solving equation of tangent and the curve for point of intersection c x+1 +x=3 ...(ii) Solving Eqs. (i) and (ii), x=1 On putting this in Eq. (ii), we get c=4

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