Easy second derivative question

In summary, the conversation discusses a solved easy second derivative question involving a given equation and answer choices. The question is about finding the second derivative of the equation, and the conversation includes steps and explanations to arrive at the correct answer. The conversation also expresses gratitude towards the helpful responders.
  • #1
demersal
41
0
[SOLVED] easy second derivative question

Homework Statement


"If y^2 - 3x =7 what is the second derivative?"

Homework Equations



Answer choices:

A) -6/7y^3
B) -3/y^3
C) 3
D) 3/2y
E) -9/4y^3


The Attempt at a Solution



I got the first derivative to be: 3/2y
Second derivative: -6/(4y^2)

I cannot for the life of me figure out what I did wrong, but I know it's something since that's not a choice. I've been messing up a lot lately, so I think I'm making some sort of vital error. A step by step explanation would be appreciated!

You guys are so awesome here, thank you for all that you do.
 
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  • #2
If y'=3/(2y)=(3/2)*y^(-1) (and it is) then y''=(3/2)*(-1)*y^(-2)*y'. Notice the y' on the right side coming from the chain rule. Now substitute your previous expression for y' for that y'.
 
  • #3
well the first derivative is [itex]\frac{dy}{dx}=\frac{3}{2y}=\frac{3}{2}y^{-1}[/itex]
diff. w.r.t x again

[tex]\frac{d^2y}{dx^2}=\frac{-3}{2}y^{-2}\frac{dy}{dx}[/tex]

which should give...[tex]\frac{d^2y}{dx^2}=\frac{-3}{2}y^{-2}\frac{3}{2}y^{-1}[/tex]

I think you multiplied wrongly
 
  • #4
Dick, you are beyond wonderful. I kept messing up because I wasn't subbing for y' properly, but now I see the trick to use the first derivative.

THANK YOU!
 

1. What is the definition of a second derivative?

The second derivative of a function is the derivative of the first derivative. It measures the rate of change of the slope of the function, or the rate of change of the rate of change of the original function.

2. How do you find the second derivative of a function?

To find the second derivative of a function, you first take the derivative of the original function to find the first derivative. Then, you take the derivative of the first derivative to find the second derivative. This can be done using the power rule, product rule, quotient rule, or chain rule.

3. What does the second derivative tell us about a function?

The second derivative tells us about the curvature of a function. A positive second derivative indicates that the function is concave up, while a negative second derivative indicates that the function is concave down. The second derivative can also help determine the inflection points of a function.

4. How do you interpret the second derivative on a graph?

The second derivative can be interpreted as the slope of the slope of the original function. On a graph, the second derivative can be represented by the curvature of the function. A positive second derivative results in a upward curvature, while a negative second derivative results in a downward curvature.

5. Why is the second derivative important in calculus?

The second derivative is important in calculus because it allows us to analyze the behavior of a function in more detail. It helps us determine the maximum and minimum values of a function, as well as the points of inflection. The second derivative also plays a crucial role in optimization problems and curve sketching.

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