AP EAMCET202124 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

For the curve y=5 x-2 x^3 , if x increases at the rate of 2 units/sec, the rate of change in the slope of the curve at x=3 is ......../sec

Options

A72
B27
C-72
D-27

Correct answer

C. -72

Step-by-step solution

y=5 x-2 x^3 d y d x =5-6 x^2 Slope of curve is 5-6 x^2 . m=5-6 x^2 d m d t =(-12 x) d x d t ( d m d t )_ x=3 =-12(3) 2=-72 [ d x d t =2 ] Rate of change of slope at x=3 is -72

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