to approximate f(-1.1), let ∆x = -0.1 and you have
∆y/∆x ≈ dy/dx
∆y ≈ dy/dx * ∆x
dy/dx at x = -1 is (4*(-1)^2))/((-1)^3+3) = 4/2 = 2
so, ∆y ≈ 2(-0.1) = -0.2
thus, y(-1.1) ≈ y(-1) + ∆y = -3 - 0.2 = -3.2
If f(-1)=-3 and f'(x)=(4x^2)/(x^3+3), which of the following is the best approximation for f(-1.1) using local linearization?
a) -7.2
b) 2.8
c) -1.2
d) -3.2
1 answer
1 answer