Value of second derivative at a given point?

In summary, the second derivative d2y/dx2 can be evaluated using the formula (4(dy/dx) -12x^2 -12y^2(dy/dx)^2)) /(4y^3 - 2x) at a given point (1,1). The resulting answer is -14. The question may involve using the X2 button and the value of dy/dx may be necessary to solve it. The final exam is this Friday and any help in finding the answers would be greatly appreciated.
  • #1
ashina14
34
0
I'm not sure how to evaluate the second derivative

d2y/dx2 = (4(dy/dx) -12x^2 -12y^2(dy/dx)^2)) /(4y^3 - 2x)
AT A GIVEN POINT (1,1). The answer is -14 not sure how they got it.

Final exam this friday would appreciat e answers very much!
 
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  • #2
hi ashina14! :smile:

(try using the X2 button just above the Reply box :wink:)

what is the complete question? :confused:
 
  • #3
Didn't occur to me that the value of dy/dx would play a role. But it is -1 and now I know I just need to substitute it in this equation wherever appropriate! Stupid question! :P
 

FAQ: Value of second derivative at a given point?

What is the second derivative of a function?

The second derivative of a function is the derivative of the first derivative. It represents the rate of change of the slope of a function at a given point. In other words, it shows how much the slope is changing at that specific point.

Why is the second derivative important?

The second derivative is important because it can help determine the concavity of a function, which can provide valuable information about the behavior of the function. It can also be used to find the inflection points of a function, where the concavity changes.

How is the second derivative calculated?

The second derivative can be calculated by taking the derivative of the first derivative using the same process as finding the first derivative. This involves using the power rule, product rule, quotient rule, and chain rule as needed.

What does the value of the second derivative at a given point tell us?

The value of the second derivative at a given point tells us the rate of change of the slope at that point. If the value is positive, the slope is increasing, and if the value is negative, the slope is decreasing. A value of zero indicates a point of inflection.

How can the second derivative be used in real-life applications?

The second derivative can be used in various fields such as physics, economics, and engineering to analyze and predict the behavior of systems. For example, in physics, the second derivative of an object's position with respect to time can be used to determine its acceleration.

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