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if f(x) = 4x^2 - 16ln(x-1) - 10, find f'(x) and hence solve the equation f'(x)=0.

f(x) = 4x² - 16ln(x-1) -10, f'(x) = 8x - 16/(x-1), so if f'(x)=0, then 8x - 16/(x -1)=0, 8x(x-1) - 16 = 0, 8x²- 8x - 16 =0, 8(x²- x - 2) = 0, x²- x - 2 = 0, (x - 2)(x + 1) =0, so x = 2 and x = -1

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