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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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2.4 Rates of Change and Tangent Lines Devil’s Tower, Wyoming Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993.

2.4 Rates of Change and Tangent Lines Devil’s Tower, Wyoming Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993.

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