# Chapter 2 - Differentiation - 2.1 Exercises: 31

$\\y=\frac{3}{4}x-2$

#### Work Step by Step

$\\f(x)=x+\frac{4}{x}$ $\\f(x)=x+4x^{-1}$ $\\f'(x)=1-4x^{-2}$ $\\f'(x)=1-\frac{4}{x^2}$ $\\f'(-4)=1-\frac{4}{(-4)^2}$ $\\f'(-4)=1-\frac{1}{4}$ $\\f'(-4)=\frac{3}{4}$ Apply to straight line equation (y-y1)=m(x-x1) $\\y+5=\frac{3}{4}(x+4)$ $\\y+5=\frac{3}{4}x+3$ $\\y=\frac{3}{4}x-2$

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