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se considera functia f(x)=(x-5)(x-4)(x-3)(x-2)+1
aratati ca f'(5)=6


Răspuns :

Răspuns:

f(x)=(x-5)(x-4)(x-3)(x-2)+1=

(x²-5x-4x+20)(X²-3x-2x+6)+1+

(x²-9X+20)(x²-5X+6)+1=

X⁴-9x³+20x²-5x³+45x²-100x+10+1

x⁴-14x³+65X²-100x+1

f `(x)=4x³-42x²+130x-100

f `(5)=4*125_42*25_130*5-100

500-1090-650

Explicație pas cu pas: