Question

Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate.f(x)=7e^(−x), a = −0.1

Set the center of the linearization as x=0.

Answer 1

Linearization of y = f(x) at a center x = b is given by,

we have to find the linearization at a center b = 0 Hence we can write,

   ----------------------------------------------------------1)

we have f(x) = 7e^-x hence we can write,

Hence,

we have f(0) = 7 and f'(0) = -7 put them in equation 1) we can write,

It means we can write linearization of f(x) = 7e^-x centered at b = 0 is given by,

Hence we can write,