Question

what is the linear approximation of f(x)=x^3-x at x=2

Answer 1

dy/dx = 3 x^2 - 1
at x = 2, dy/dx = 3*4-1 = 11
so m, the slope, = 11
at x = 2, y = 8 - 2 = 6
so
we need a line of form y = m x + b
with slope m = 11
that goes through the point (2,6)