# Help Needed: Differentiation in Maths - Find F(x) & t(x)

• VooDoo
In summary: This does not provide an alternative to the previous method, but rather shows the error in using the tangent line as an approximation.
VooDoo
We did this new mathematics thing in class today which I did not understand, it came under the topic of differentiation.

Firstly we were given the equation

f(x)=E^x

Then find the value of F(x) for x=0
F(0)=E^0
F(0)=1
therefore (0,1)

Then it said find the equation of the tangent at x=0

Which I worked out to be Y(tangent)=X+1 [I will call this equation t(X)]

Then it said draw up a table ranging from -.2 to .2 with increments of 0.05 for the equation

[f(x)-t(x)/f(x)]*100

Now my question is what the hell are we finding here??

Thanks in advance for any help.

Who's t(x)...?

Daniel.

First of all, it is "e", not "E". Mathematically, small and capital letters may represent very different things.

Second: "Then it said draw up a table ranging from -.2 to .2 with increments of 0.05 for the equation

[f(x)-t(x)/f(x)]*100

Now my question is what the hell are we finding here??"

My question is "what the hell are you talking about??"
You haven't told us what t(x) is! I suspect that you meant t(x) to be x+ 1, the tangent line. In that case, you are finding the percentage error in using the tangent line to approximate ex around x=0.

HallsofIvy said:
First of all, it is "e", not "E". Mathematically, small and capital letters may represent very different things.

Second: "Then it said draw up a table ranging from -.2 to .2 with increments of 0.05 for the equation

[f(x)-t(x)/f(x)]*100

Now my question is what the hell are we finding here??"

My question is "what the hell are you talking about??"
You haven't told us what t(x) is! I suspect that you meant t(x) to be x+ 1, the tangent line. In that case, you are finding the percentage error in using the tangent line to approximate ex around x=0.

Thanks for that, just what I was after. I mentioned what t(x) was but I agree it was not clear enough.

Hmm, HallsofIvy do you know any alternatives to this method?

Differentials can approximate functions at a specific point.

$$\Delta y \approx f'(x) \Delta x$$

The change in a function at near point $f(x)$ is approximately the numerical derivative at x multiplied by the small change of x.

Here is what I guess you were supposed to be doing:
1) Let $$f(x)=e^{x}$$
2) The best linear approximation to f(x) at x=0 is given by $$t(x)=f(0)+f'(0)(x-0)=x+1$$
this is also called the tangent line to f at x=0
3) You are now to find the PERCENTWISE RELATIVE ERROR E(x) between f(x) and t(x) at the interval given:
$$E(x)=(\frac{f(x)-t(x)}{f(x)})*100$$

## 1. What is differentiation in math?

Differentiation is a mathematical process that allows us to find the rate of change of a function. It involves determining the instantaneous rate of change of the function at a specific point by calculating its derivative.

## 2. How do I find F(x) and t(x) in differentiation?

To find F(x) and t(x) in differentiation, you need to first identify the given function and its independent variable. Then, you can use the rules of differentiation, such as the power rule or product rule, to calculate the derivatives of F(x) and t(x).

## 3. What are the applications of differentiation in real life?

Differentiation has many applications in real life, including in physics, engineering, economics, and statistics. It is used to model and analyze various phenomena, such as motion, growth, and optimization.

## 4. What are some common mistakes to avoid in differentiation?

Some common mistakes to avoid in differentiation include forgetting to use the chain rule, not simplifying the derivative expression, and making careless errors in calculations.

## 5. Is there a shortcut or trick to solving differentiation problems?

While there is no specific shortcut or trick to solving differentiation problems, it is important to have a strong understanding of the basic rules and concepts. Practice and familiarity with different types of functions can also make the process easier and quicker.

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