Question

Задачи по алгебре по производной ​

Answer 1

$\displaystyle\bf\\1=\\V(t)=-\frac{5}{3} t^{3}+\frac{15}{2} t^{2} +50t+70\\\\\\P(t)=V'(t)=-\frac{5}{3} \cdot(t^{3} )'+\frac{15}{2} \cdot(t^{2} )'+50\cdot t'+70'=\\\\\\=-\frac{5}{3} \cdot 3t^{2}+\frac{15}{2} \cdot2t+50\cdot 1+0=-5t^{2} +15t+50\\\\\\P(2)=V'(2)=-5\cdot2^{2} +15\cdot2+50=-20+30+50=60\\\\\\2)\\P(t)=\frac{t^{2} }{2} +3t-3\\\\\\V(t)=P'(t)=\frac{1}{2} \cdot(t^{2} )'+3\cdot t'-3'=\frac{1}{2}\cdot2t+3-0=t+3\\\\\\V(3)=3+3=6\\\\\\3)$

$\displaystyle\bf\\X(t)=3000+100t^{2} \\\\\\V(t)=X'(t)=3000'+100\cdot(t^{2} )'=0+100\cdot 2t=200t\\\\\\V(1)=200\cdot 1=200$