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Maths
Scottish Highers

show y=3x-5 is tangent to x^2 + y^2 +2x -4y - 5 = 0 and the point where they touch

y=3x-5x^2 + (3x-5)^2 + 2x - 4(3x-5) - 5 = 0x^2 + 9x^2 -30x +25 + 2x -12x + 20 - 5 = 010x^2 -40x + 40 = 010 (x^2 - 4x +4) = 010(x - 2)^2 = 0x=2implies one point of contact, therefore tangenty = 3x - 5y = 6...

Answered by Robert M. Maths tutor
1931 Views

Given f(x) = (x^(2)+(3*x)+1)/(x^(2)+(5*x)+8), find f'(x) and simplify your answer.

Taking: f(x) = (x^(2)+(3x)+1)/(x^(2)+(5x)+8)
An application of the quotient rule of differentiation is required. This rule is given as:
Where g(x) = u(x)/v(x), g'(x) = ((u'(x)v(x))...

Answered by Andrew M. Maths tutor
1290 Views

Differentiate 5x^2 - 7x +9

The general rule for differentiation is multiply by the power and decrease the power by one.
So if we take each term individually starting with 5x^2, and multiply by the power giving 10 then reduce t...

Answered by Rachael G. Maths tutor
1209 Views

Differentiate (with respect to x), y=2x^2+8x+5.

y= 2x^2 + 8x + 5 is a simple quadratic equation and can be easily differentiated. Consider it in different terms working from left to right: y converts to dy/dx. This just means ‘differentiate y with resp...

Answered by Jack D. Maths tutor
946 Views

Given that dy/dx = 6x*2 - 3x + 4 And y =14 when x=2. Express y in terms of x

Dy/dx = 6x2- 3x + 4y = 12x - 3 + c14 = 12(2) - 3 + (c)14= 24 - 3 + c14 = 21 + cc= -7y = 12x - 10

Answered by Medi N. Maths tutor
2024 Views

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