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The curve ypx2 plus qx plus к has a maximum turning point at 2 18 If 0 10 is a point on the curve find the value of p q and r?
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ypx2+qx+k is NOT an equation of a curve!
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Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
What is the word maximum in math?
In mathematics, the term "maximum" refers to the largest value in a given set of numbers or the highest point of a function within a specified domain. It can be used in various contexts, such as finding the maximum value of a dataset, the maximum height of a curve, or the optimal solution in optimization problems. The maximum can be either absolute (the highest value overall) or relative (the highest value in a local neighborhood).
What is the highest point of a graph?
The highest point of a graph is called the "maximum" or "local maximum" if it is the highest point within a certain interval. It represents the greatest value of the function at that point, often indicating a peak or turning point. In a broader sense, the absolute maximum refers to the highest point over the entire graph. Identifying this point is crucial in optimization problems and analyzing the behavior of functions.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
What is the bottom of a curve called?
The bottom of a curve is typically referred to as its "minimum" point. In the context of mathematics or graphing, this is the lowest point on the curve, where the value is less than or equal to all nearby points. In some cases, it can also be called a "valley" if the curve forms a U-shape around that point.
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
How do you find minimum and maximum value of calculus?
For the function y = x^(3) + 6x^(2) + 9x Then dy/dx = 3x^(2) + 12x + 9 At max/min dy/dx = 0 Hence 3x^(2) + 12x + 9 = 0 3(x^(2) + 4x + 3) = 0 Factor (x + 1)(x + 3) = 0 Hence x = -1 & x = -3 are the turning point (max/min) To determine if x = 0 at a max/min , the differentiate a second time Hence d2y/dx2 = 6x + 12 = 0 Are the max/min turning points. Substitute , when x = -1 6(-1) + 12 = (+)6 minimum turning point . x = -3 6(-3) + 12 = -6 maximum turning point. When x = positive(+), then the curve is at a minimum. When x = negative (-), then the curve is at a maximum turning point. NB When d2y/dx2 = 0 is the 'point of inflexion' , where the curve goes from becoming steeper/shallower to shallower/steeper. So when d2y/dx2 = 6x + 12 = 0 Then 6x = -12 x = -2 is the point of inflexion. NNB When differentiating the differential answer gives the steeper of the gradient. So if you make the gradient zero ( dy/dx = 0) , there is no steepness, it is a flat horizontal line
What is the word maximum in math?
In mathematics, the term "maximum" refers to the largest value in a given set of numbers or the highest point of a function within a specified domain. It can be used in various contexts, such as finding the maximum value of a dataset, the maximum height of a curve, or the optimal solution in optimization problems. The maximum can be either absolute (the highest value overall) or relative (the highest value in a local neighborhood).
What does the derivative at a point mean?
The derivative at any point in a curve is equal to the slope of the line tangent to the curve at that point. Doing it in terms of the actual expression of the curve, find the derivative of the curve, then plug the x-value of the point into the derivative to find the derivative at that point.
What is the highest point of a graph?
The highest point of a graph is called the "maximum" or "local maximum" if it is the highest point within a certain interval. It represents the greatest value of the function at that point, often indicating a peak or turning point. In a broader sense, the absolute maximum refers to the highest point over the entire graph. Identifying this point is crucial in optimization problems and analyzing the behavior of functions.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
What is a point on a curve?
A point on a curve is a specific location defined by its coordinates in a given coordinate system, such as Cartesian or polar coordinates. It represents a unique value or set of values for the independent variable(s) that determine the position on the curve. For example, on a graph of a function, a point might correspond to an input (x-value) and its resulting output (y-value), illustrating the relationship defined by the curve.
What is the slope of a curve line?
The slope of a curved line changes as you go along the curve and so you may have a different slope at each point. Any any particular point, the slope of the curve is the slope of the straight line which is tangent to the curve at that point. If you know differential calculus, the slope of a curved line at a point is the value of the first derivative of the equation of the curve at that point. (Actually, even if you don't know differential calculus, the slope is still the value of the function's first derivative at that point.)
How can one determine the pKa from a titration curve?
To determine the pKa from a titration curve, identify the point on the curve where the pH is equal to the pKa value. This point represents the halfway point of the buffering region, where the concentration of the acid and its conjugate base are equal.
What is amplituide?
amplitude can be defined as the maximum value of varying quantity . the varying quantity can be an alternating one or distorting. graphically speaking the maximum value of the curve within the extremes of a domain is called as the amplitude..
What is the bottom of a curve called?
The bottom of a curve is typically referred to as its "minimum" point. In the context of mathematics or graphing, this is the lowest point on the curve, where the value is less than or equal to all nearby points. In some cases, it can also be called a "valley" if the curve forms a U-shape around that point.
How do you calculate KD from a binding curve?
To calculate the dissociation constant (KD) from a binding curve, you can use the equation KD C50, where C50 is the concentration of the ligand at which half of the binding sites are occupied. This value can be determined by plotting the binding data and finding the point where half of the maximum binding is achieved.
