Question

10 клас номер 20.11 - первое номер 20.12-второе

Answer 1

$1)f(x)=\frac{1}{3}x^{3}+x^{2}\\\\f'(x)=\frac{1}{3}(x^{3})'+(x^{2})'=\frac{1}{3} *3x^{2} +2x=x^{2}+2x\\\\f'(x_{o})=f'( -1)=(-1)^{2}+2*(-1)=1-2=-1$

$g(x)=2Ctgx\\\\g'(x) =2(Ctgx)'=2*(-\frac{1}{Sin^{2}x })=-\frac{2}{Sin^{2}x }\\\\g'(x_{o})=g'(-\frac{\pi }{4})=-\frac{2}{Sin^{2}(-\frac{\pi }{4}) }=-\frac{2}{(\frac{1}{\sqrt{2} })^{2}}=-4$