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Differentiate to get:dy/dx = 12x^3 -24x^2Factorise and set equal to 0:12x^2(x-2) = 0Solve to get x = 2 and x =0.

Integrate by parts once to obtain: xe^x - e^x + c

First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our fu...

dy/dx = 2x -2 -12x^(-1/2)

We first differentiate f(x), and we get f'(x)=2x + 5. We then set this equal to 0 and then solve for x. We get that xmin= -2.5. We check whether this was indeed a minimum, by calculating the second deriva...