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What is the equation of the tangent drawn to the curve y = x^3 - 2x + 1 at x = 2?

The equation of a two-dimensional non-vertical line can easily be determined if its gradient 'm' and a point on the line (x0, y0) is known, using the formula m = (y - y0) / (x - x0). The gradient of the tang...
MZ
Answered by Mario Z. • Maths tutor
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Why does the product rule for differentiating functions work?

Let k(x) = f(x)g(x) then k'(x) = limit as h --> 0 of: (h(x+h)-h(x))/h = lim (f(x+h)g(x+h) - f(x)g(x))/h We can factorise the numerator as: f(x+h)g(x+h) - f(x)g(x) =f(x+h)g(x+h) -g(x)f(x+h) + g(x)f(x+h)- f...
BV
Answered by Blaine V. • Maths tutor
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Given that y = 16x^2 + 7x - 3, find dy/dx [3 marks]

32x + 7
BH
Answered by Bodrul H. • Maths tutor
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How do I form an algebraic fraction into a single fraction in its simplest form?

When starting with a fraction with 2 individual components, before any addition, subtraction or simplification can take place, the first step will be making them both having the same denominator. Once you ha...
AS
Answered by Axel S. • Maths tutor
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Express (16x^2 + 4x^3)/(x^3 + 2x^2 - 8x) + 12x/(x-2) as one fraction in its simplest form.

Answer: 16x/(x - 2) Start with the numerator of the first fraction, 16x 2 + 4x 3 , take a factor of 4x 2 out to get 4x 2 (4 + x). Then look at the denominator of the fraction, x 3 + 2x 2 - 8x, immediately yo...
MS
Answered by Manon S. • Maths tutor
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