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**CALCULUS The derivative and the applications of differentiation**

Clil Activity 1

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**First of all: HOW DO YOU SAY IT?**

…a very useful website... …Let’s use it!

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**For the function f, the formula:**

DIFFERENCE QUOTIENT (also called «Average Rate of Change») For the function f, the formula: This formula computes the slope of the secant line through two points of the graph of f. These are points with x-coordinates x and x+h. The difference quotient is used in the definition of the derivative. … so far so good.

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**Is this the definition we gave a few weeks ago? What is this?**

DERIVATIVE A function which gives the slope of a curve; that is, the slope of the line tangent to a function. Is it all? Is this the definition we gave a few weeks ago? What is this?

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**Now we have to learn how to read it.**

«The difference quotient is used in the definition of the derivative.» So, why don’t we use it? Now we have to learn how to read it.

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**The third one just looks like a**

We may use another interesting website: The third one just looks like a tongue-twister…

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**We may use another interesting website: http://online. scuola**

Try to write in words the definition of derivative and read it using these tips.

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«The derivative of f of x equals the limit, for h that tends to zero, of f of x plus h minus f of x all over h»

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EXERCISE 1 Read the task. Is there any new word? What is the GRADIENT of a curve and how can you find it? Solve the exercise and then share the results.

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**to solve the 2nd exercise.**

Now you’re ready to solve the 2nd exercise.

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1.4 – Differentiation Using Limits of Difference Quotients

1.4 – Differentiation Using Limits of Difference Quotients

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