Question

Вычислите значение производной функции f(x) = -5x^9-2x^6=+7x^2+7x в точке х0=-1

Answer 1

$f(x)=-5x^9-2x^6+7x^2+7x\ \ ,\ \ x_0=-1\\\\\\f(-1)=5-2+7-7=3\\\\f'(x)=-45x^8-12x^5+14x+7\\\\f'(-1)=-45+12-14+7=-40\\\\\\\underline {\ y=f(x_0)+f'(x_0)(x-x_0)\; }\\\\y=3-40(x+1)\\\\\underline {\ y=-40x-37\ }$