The best way to sketch a graph of the function y -2x 2-4x-6 is to first get the values of Y and X and then use the values to sketch the graph.
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The derivative of a function is the function's tangent function.So, d(y)/dx = d(2tan(2x))/dx = 2*d(tan(2x))/dx = 2*d(tan(u))/du*du/dx, where u=2x, = 2*sec2(2x)*d(2x)/dx = 4*sec2(2x)*d(x)/dx = 4*sec2(2x)Now just make a plot for y = 4*sec2(2x) and you got your tangent function.
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
Y = 2X + 8 is a linear function of the form, Y = mX + c. A line.
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The rate of change for the linear (not liner) function, y = 2x +/- 3 is 2.