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What is the point of differentiation?

Differentiation is a very useful concept; informally it tells us how 'fast' something is changing. A real-life example is given by the first and second derivatives of distance with respect to time: the fi...

Answered by Jake H. • Maths tutor

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A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.

To calculate the minimum value of A we first need to establish an equation for A. The surface area of a cuboid is relatively simple to figure out we simply work out the area of the faces and sum them toge...

Answered by Jacob C. • Maths tutor

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Solve the simultaneous equations y + 4x + 1 = 0 and y^2 + 5x^2 + 2x = 0

y=-4x-1
(-4x-1)^2 +5x^2 +2x=0

16x^2 +8x +1 +5x^2 +2x=0

21x^2 +10x + 1 =0
(7x+1)(3x+1)=0

x=-1/7 or -1/3

y= -3/7 or 1/3

Answered by Dinesh J. • Maths tutor

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The curve A (y = x3 – x2 + x -1) is perpendicular to the straight-line B at the point P (5, 2). If A and B intersect at P, what is the equation of B? Also, find any stationary points of the curve A.

Firstly find the gradient of A, through differentiation: dy/dy = 3x² – 2x + 1. To find the gradient at P, substitute the x value of the P coordinate into this equation: dy/dx = 3(2)²...

Answered by James S. • Maths tutor

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