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2.925 minutes This question involves solving a first order differential equation via the separation of variables and then substituting in initial conditions in order to find a particular ...

To find the minimum point of this curve you need to differentiate y and set it equal to zero before solving for x. If the questions does not say otherwise give your answer to 3 s.f. dy/dx = 3e^3x -12e^2x ...

let u = x^2              let v  = e^2x

du/dx = 2x             dv/dx = 2e^2x

d/dx = vdu/dx + udv/dx = 2x e^2x + 2x^2e^2x

Therefore

d/dx = ...

Differentiation is the rate of change of one variable with respect to another at a point in time or space. In other words, this can be described as the slope of a curve, which is how much the curve goes u...

So here we want to eliminate one variable so we are only working with either x or y by themself, so to do this we can rearrange the first equation of x+y=1 to x= 1-y. This new equation can therefore be su...