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Find the x coordinate of the minimum point of the curve y = e3x - 6e2x + 32.

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 = 0...
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Answered by Hermione W. • Maths tutor
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Differentiate the function f(x) = x^2 * e^2x with respect to x

l e t u = x^2 let v = e^2x du/dx = 2x dv/dx = 2e^2x d/dx = v du/dx + u dv/dx = 2x e^2x + 2x^2 e^2x Therefore d/dx = 2x*e^2x * (1 + x)
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Answered by Evan S. • Maths tutor
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What is differentiation in mathematics and what does it represent?

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 up o...
MB
Answered by Marius B. • Maths tutor
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Solve the simultaneous equations x + y = 1 , x^2 -2xy+y^2=9

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 subst...
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Answered by Belinda S. • Maths tutor
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The line AB has equation 5x + 3y + 3 = 0. The line AB is parallel to the line y = mx + 7. Find the value of m.

Rearrange AB into y = mx + c format: 1) 3y = -3 - 5x 2) y = - 5/3 x - 1 Compare equation with y = mx + c Conclude m = - 5/3 You can also deduce the y-intercept of AB is -1.
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Answered by Emanuel D. • Maths tutor
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