Question

найдите эластичность функции f(x)=cos(-5x-5)/(4x^2-x-4) в точке а=-1

Answer 1

$E_y=frac{x}{y}*y' \ y'=(frac{cos(-5x-5)}{4x^2-x-4})'=(frac{cos(5x+5)}{4x^2-x-4})'=\ =frac{-5sin(5x+5)(4x^2-x-4)-cos(5x+5)(8x-1)}{(4x^2-x-4)^2}\ E_y=frac{x(4x^2-x-4)}{cos(5x+5)}*frac{-5sin(5x+5)(4x^2-x-4)-cos(5x+5)(8x-1)}{(4x^2-x-4)^2}=\ =frac{x}{cos(5x+5)}*frac{-5sin(5x+5)(4x^2-x-4)-cos(5x+5)(8x-1)}{4x^2-x-4}$

$E_y(-1)=frac{-1}{cos0}*frac{-5sin0*(-4)-cos0*(-9)}{1}=-1*9=-9$