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Yes, the concavity of a curve can be determined by differentiation. To find out the concavity of a graph at various points, you want to analyze the second derivative (f''(x)). Take the derivative of your original equation, then, take the derivative of this equation. By setting this second derivative to zero, you can solve for the critical points (x-intercepts/asymptotes) of the second derivative graph. Once these critical points are found, make a number line with these points marked. By doing a sign test on either sides of the critical points (plug in numbers below and above the critical points into the second derivative equation), you can find the concavities of your original graph. Wherever the sign tests results in a positive number, that is where a upward facing curve is (concave up); where it is negative, that is where a concave down portion is.
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What Is Point Of Inflection?
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes.
Is there any application of differentiation in statistics?
Yes. For example, consider a standard normal curve. z = 1 and z = -1 happen to lie at the inflection points of the normal curve.
How do you find the exact value of the gradient of the curve with equation y equals 1 divide by 4 minus x2 at the point where x equals 1 over 2?
You find the gradient of the curve using differentiation. The answer is 0.07111... (repeating).
What is the adjective of the word regression?
of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
What is the principle of differentiation?
Differentiation of funtion is rate of chnage of that funtion.
What Is Point Of Inflection?
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes.
What does the second order differential equation represent graphically?
actually it represents the concavity or convexity of a curve
What is another word for depression or indentation?
Another word for depression or indentation is "concavity." Concavity refers to a surface that curves inward or has a depressed area. It is commonly used in mathematics and geometry to describe the shape of a curve or surface that is curved inward rather than outward.
Is there any application of differentiation in statistics?
Yes. For example, consider a standard normal curve. z = 1 and z = -1 happen to lie at the inflection points of the normal curve.
What is the meaning of Concavity and convexity?
Concavity refers to a shape that curves inward or has a "cave-like" appearance, such as a frown. Convexity, on the other hand, refers to a shape that curves outward or bulges, like a smile. In mathematics, concavity and convexity describe the shape of a curve based on its curvature.
Why is long run average cost curve known as the planning curve?
The long run average cost curve will help the company plan for product differentiation. With knowledge of a particular cost curve, the company can plan complement products to make up for deficits in profit margins.
Which most accurately describes how the equilibrium price of a good or a service can be determined?
By finding where the supply curve and the demand curve intersect.
Which the following most accurately describes how the equilibrium prices of a good or service can be determined?
By finding where the supply curve and the demand curve intersect.
How do you find the exact value of the gradient of the curve with equation y equals 1 divide by 4 minus x2 at the point where x equals 1 over 2?
You find the gradient of the curve using differentiation. The answer is 0.07111... (repeating).
What effect would a decrease in production costs for all firms have on the aggregate supply curve?
the curve would shift to the right
Why is it that the sun appears yellow?
That is about where the peak of its blackbody radiation curve is, as determined by the photosphere temperature.
How can you tell if a linear appoximation is too large or too small?
The precision of a linear approximation is dependent on the concavity of the function. If the function is concave down then the linear approximation will lay above the curve, so it will be an over-approximation ("too large"). If the function is concave up then the linear approximation will lay below the curve, so it will be an under-approximation ("too small").
