OEF derivada --- Introducció ---

The derivative of a combined function

=

NB : write "sqrt(ax+b)" for

The derivative of a polynomial

The product rule

In order to determine the derivative of   we apply the following rule of differentiation:

The derivative function of   will be :

The quotient rule

• We rewrite as a fraction; ,wherein the functions and are defined in by :  and 

• The functions and are differentiable in :  and 
• = met :

   en 

   and 

• The fraction is differentiable in:
• Which rule on differentiation do we apply :
• is differentiable in .
• Which rule on differentiation do we apply :
• We will get : =

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Tangent and derivative

Given the plane . The curve C is the graph of the function     , defined in . The line is the tangent of C in point , with coordinates ( : ). Point , with coordinates ( : ) is also on line . Determine the value of     at two decimals accurate.

xrange -, yrange -, parallel -,-,-,,1,0, 2*+1, grey parallel -,-,,-,0,1, 2*+1, grey hline 0,0,black vline 0,0,black arrow 0,0,1,0,8, black arrow 0,0,0,1,8, black text black , -0.5,-0.3,small , O text black , 1,-0.3,small , I text black , -0.5,1,small , J text blue , -+0.5 , , medium, y=f(x) linewidth 1.5 plot blue, plot green,

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Investigate a Function

Given the function defined in by   . Investigate this function and determine the extremum (extrema) of .

1. The function is differentiable in :
   for all real
2. The nature of the derivative function is zero for =
1. The derivative of
2. The nature of the sign of - + 0
3. The nature of the sign of is on the interval
4. is on the interval

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