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The tangent to 2x3 - 3x2 - 8x + 9 at x = 2 is y = 4x - 11
The tangent to y = 2x3 - 3x2 - 8x + 9 at x = 2 has the same gradient as the curve at that point; to find the gradient, differentiate:
dy/dx = 6x2 - 6x - 8
which at x = 2 is:
gradient = 6 x 22 - 6 x 2 - 8 = 4
At x = 2, y = 2 x 23 - 3 x 22 - 8 x 2 + 9 = -3
The equation of a line through point (xo, yo) with gradient m is:
y - yo = m(x - xo)
Thus the equation of the tangent to the line at x = 2 is:
y - -3 = 4(x - 2)
⇒ y = 4x - 11
What else can I help you with?
What is the point of contact when the tangent line y equals x plus c touches the curve y equals 3x -x -5x squared?
-2
What kind of equation is ax plus b equals 0 in?
A linear equation.
What is x plus y equals 11?
It is an equation of a straight line.
What are the tangent line equations of the circle x2 plus y2 -6x plus 4y plus 5 equals 0 when the circle passes through the x axis?
Equation of circle: x^2 +y^2 -6x +4y +5 = 0 Completing the squares: (x-3)^2 +(y+2)^2 = 8 Radius of circle: square root of 8 Center of circle: (3, -2) Circle makes contact with the x axis at: (1, 0) and (5, 0) Slope of 1st tangent: 1 Slope of 2nd tangent: -1 1st tangent line equation: y = 1(x-1) => y = x-1 2nd tangent line equation: y = -1(x-5) => y = -x+5
What is the equation of 3d plus 14 equals 11?
3d + 14 = 11 is the equation.
An equation of the line tangent to the graph of y equals x3 plus 3x2 plus 2 at its point of inflection is?
(a) y = -3x + 1
What is the radius equation inside the circle x squared plus y squared -8x plus 4y equals 30 that meets the tangent line y equals x plus 4 on the Cartesian plane showing work?
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
What is the tangent equation of the circle x2 plus 10x plus y2 -2y -39 equals 0 at the coordinate of 3 2?
Equation of circle: x^2 +10x +y^2 -2y -39 = 0 Completing the squares: (x+5)^2 +(y-1)^2 = 65 Center of circle: (-5, 1) Point of contact: (3, 2) Slope of radius: 1/8 Slope of tangent: -8 Tangent equation: y-2 = -8(x-3) => y = -8x+26
What is the tangent line equation that passes through the origin touching the circle x2 plus y2 plus 6x -10y equals 0?
Circle equation: x^2 +y^2 +6x -10y = 0 Completing the squares: (x +3)^2 +(y -5)^2 = 34 Center of circle: (-3, 5) Point of contact: (0, 0) Slope of radius: -5/3 Slope of tangent line: 3/5 Tangent line equation: y = 0.6x
Equation that can be expressed in the form of the equation y equals ax2 plus bx plus c?
A quadratic equation.
What is the value of k when the straight y equals 3x-1 is a tangent to the curve x squared plus y squared equals k?
2
What is the equation for -d plus 7 equals 3?
That's the equation.
What is the value of k when y equals 3x plus 1 and is a line tangent to the curve of x squared plus y squared equals k?
k = 0.1
What is the solution for the equation -x plus y equals 4 and the equation 2x plus y equals 4?
x = 0 and y = 4
How do you prove that the line y equals x-4 is tangent to the curve of x squared plus y squared equals 8?
equation 1: y = x-4 => y2 = x2-8x+16 when both sides are squared equation 2: x2+y2 = 8 Substitute equation 1 into equation 2: x2+x2-8x+16 = 8 => 2x2-8x+8 = 0 If the discriminant of the above quadratic equation is zero then this is proof that the line is tangent to the curve: The discriminant: b2-4ac = (-8)2-4*2*8 = 0 Therefore the discriminant is equal to zero thus proving that the line is tangent to the curve.
What is the Equation for alcoholic fermentation?
The summary equation is the formula equation. Sugar equals alcohol plus carbon dioxide. The formula is C6H12O6 which equals 2 CH3CH2OH plus 2 CO2.
What is the tangent equation at the point of 1 -1 when it touches the circle of 2x2 plus 2y2 -8x -5y -1 equals 0?
The tangent equation that touches the circle 2x^2 +2y^2 -8x -5y -1 = 0 at the point of (1, -1) works out in its general form as: 4x +9y +5 = 0
