# Calculus N00b: Find the Second Derivative

• gschjetne
In summary, the conversation is about finding the second derivative of a function and using proper mathematical rules to solve it. The correct answer is 12x^-4-6x^-3 and can also be written as (12-6x)/x^4. Quotient rule is mentioned as a possible way to solve the problem and the conversation ends with Daniel giving a hint to divide the final answer by x^4 to get the textbook answer.
gschjetne
One of my biggest griefs is the fact that I'm a complete n00b when it comes to maths.

I'm supposed to find the second derivate of

$$f(x) = \frac{2-3x}{x^2}$$

I started out with this:

$$f'(x) = \frac{-3}{x^2} + \frac{2-3x}{2x}$$

$$f''(x) = \frac{3}{2x} + \frac{2-3x}{2}$$

But it didn't take long until I found I was just making gibberish...
Any ideas?

Nope.Both are incorrect.U should apply the rules properly.It's easier,if u decompose.

$$f(x)=2x^{-2}-3x^{-1}$$

Can u compute the derivatives now...?

Daniel.

P.S.HINT:Just the power rule involved.

Are you familiar with the quotient rule?

Thanks.
This should be correct, then:

$$f(x)=2x^{-2}-3x^{-1}$$

$$f'(x)=-4x^{-3}+3x^{-2}$$

$$f''(x)=12x^{-4}-6x^{-3}$$

The textbook says it's $\frac{12-6X}{X^4}$, which, according to my graphing calculator identical to what I got above, but unfortunately both me and my father are lacking in skill to figure that out.

I have heard about the quotient rule, but I haven't been able to fully understand it. I'm going to ask my teacher for a tutor lesson tomorrow.

Hmm

$$\frac{12-6x}{x^{4}}=\frac{12}{x^{4}}-\frac{6x}{x^{4}}=12x^{-4}-6x^{-3}$$

Okay?

Daniel.

If you divide your final answer for f'' by x^4 you will find it gives the textbook answer ^_^

## 1. What is the purpose of finding the second derivative in Calculus?

The second derivative in Calculus is used to find the rate of change of the rate of change of a function. It can also be used to determine the concavity of a function and locate points of inflection.

## 2. How is the second derivative calculated?

The second derivative is calculated by taking the derivative of the first derivative. This can be done using the power rule, product rule, quotient rule, or chain rule depending on the complexity of the function.

## 3. What does a positive or negative second derivative indicate?

A positive second derivative indicates that the function is concave up, while a negative second derivative indicates that the function is concave down. Points where the second derivative is equal to 0 may indicate points of inflection.

## 4. How do you interpret the second derivative graphically?

The second derivative can be interpreted graphically as the slope of the slope of the original function. If the graph of the second derivative is above the x-axis, the original function is concave up. If the graph is below the x-axis, the original function is concave down.

## 5. What are some real-world applications of the second derivative?

The second derivative is commonly used in physics to analyze the acceleration of an object. It is also used in economics to analyze the marginal change in a company's profit. Additionally, the second derivative can be used in engineering to optimize the design of structures.

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