Final answer:
The linearization of the cosine function at π/2 is -x + π/2. The correct answer is d) l(x) = -cos(π/2)(x - π/2) + sin(π/2).
Step-by-step explanation:
Linearization refers to the process of approximating a nonlinear function by a linear function at a particular point. In essence, it involves creating a linear equation that closely represents the behavior of a function near a specific point on the curve.
The linearization of a function at a point a is given by the equation:
l(x) = f(a) + f'(a)(x - a)
In this case, the function is f(x) = cos(x) and the point is a = π/2. To find the linearization, we need to find the value of f(a) and f'(a).
Since f(a) = cos(π/2) = 0 and f'(a) = -sin(π/2) = -1, the linearization is:
l(x) = 0 - 1(x - π/2) = -x + π/2