Let f4 15 f4 5 Write a linearization for f with respect to

Let: f(4) = 15, f\'(4) = 5 Write a linearization for f with respect to x. Use the linearization to estimate f at x = 3.

Solution

let us assume that f(x)=ax+b which is a linear function and can be used for linearization of f(x). and a, b are constants whose values are to be found with the help of given data.

now the value of f(4)=15.

putting x=4 in f(x)

f(4)=15=4a+b .............................(1)

& f\'(4)=5 now differentiating function with respect to x

so f\'(x)=a(1)+0

f\'(x)=a at x=4

f\'(4)=a=5

a=5

now from equation 1

4*5+b=15

b= -5

so f(x)=5x-5

(end of part 1)

2. to estimate f(x) at x=3

put x=3

f(3)=5*3-5

=15-5

=10..............answer