Question

f(x) = x³ - sin(lnx + 7)
Find f'(x) or d(f(x))/dx i.e. derivative of f(x)
Also Find the maxima and minima using 2nd order derivative of f(x)

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Answer 1

Answer:

f(x)=x³-sin(logx+7)

f'(x) =[3x²-cos(logx+7)] [1/x]

f''(x)=x[6x+sin(logx+7)] -[3x²-cos(logx+7)] / x²

for maxima or minima f''(x) =0

3+sin(logx+7)+cos( logx+7)=0