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As the tangent has the same gradient as the curve at the particular point, we need to find the gradient of the curve. To find the gradient we need to differentiate. Due to there being two variables in thi...

 x^3=1=e^2(pi)ik 

x=e^2(pi)ik/3

The three roots are

k=0    x=1 

k=1    x=e^2(pi)*i/3

k=-1   x=e^-2(pi)ik/3

Approaching an analysis of a large work such as a symphony can seem daunting at first, but the task can be made easy and enjoyable by setting out what features of the music to look for (such as harmony/ m...

Firstly, note that a stationary point can either be a local maximum, local minimum or point of inflexion. Now suppose you have a differentiable function (a graph which has a unique gradient/derivative at ...

for a capacitor the equations you need to know are:  Q=CV  V=Vin*e^(t/RC) and E=1/2QV (with Q=charge/columbs, C= capacitance/Farads, V=voltage/volts, R=resitance/ohms, Vin=initial voltage when discharging...