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
Related Maths A Level answers
All answers ▸A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.
Integrate ((x^3)*lnx)dx
