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AP EAMCET201823 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

The curve f(x)=e^x x is defined in the interval [0,2 ] . The value of x for which the slope of the tangent drawn to the curve at x is maximum, is

Options

  1. A4
  2. B2
  3. C6
  4. D3

Correct answer

B. 2

Step-by-step solution

We have, f(x)=e^x x difference w.r.t ' x ' f^ (x)=e^x x+e^x x For f^ (x) is maximum we find f^ (x) aligned f^ (x)=-e^x x+e^x & x+e^x x & +e^x x=2 e^x x aligned f^ (x) is maximum at f^ (x)=0 Now, f^ (x)=0 aligned & 2 e^x x=0 & x= 2 & aligned So, slope of tangent drawn to curve is maximum at x= 2 .

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