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1. Derivabilitat


Determineu els valors de a i b que fan que la funció f(x)  sigui contínua i derivable en  tota la recta real.

f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x over 2 plus a space space space s i space x less than 0 end cell row cell x squared plus b x minus 1 space space s i space x greater or equal than 0 end cell end table close space space


a) Primer ha de ser contínua per tant, ha de passar que : stack l i m space space space with x rightwards arrow 0 to the power of minus below f left parenthesis x right parenthesis space equals space f left parenthesis 0 right parenthesis space equals stack l i m space space space with x rightwards arrow 0 to the power of plus below f left parenthesis x right parenthesis space

b) Segon ha de ser derivable o sigui :

f space apostrophe left parenthesis 0 right parenthesis space space p e r space l apostrophe e s q u e r r a space equals space f apostrophe left parenthesis 0 right parenthesis space space p e r space l a space d r e t a


Ànims

Esther


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