Hello,
I have a question regarding linear approximation.
I think I understand the overall concept, but recently there was a solution posted for a question I had on a midterm that I am unsure about.
Question:
Find a linear approximation of the function f(x)= (x-1)^1/4 at a=2 and use it to approximate (1.3)^1/4
Solution:
L(x)=f(a)+f'(a)(x-a)
=1+1/4(x-2)
L(2.3)=1+1/4(2.3-2)
=1.075
I really don't understand why 2.3 would be substituted into the equation instead of 1.3....any explanation to this would be much appreciated!
I have a question regarding linear approximation.
I think I understand the overall concept, but recently there was a solution posted for a question I had on a midterm that I am unsure about.
Question:
Find a linear approximation of the function f(x)= (x-1)^1/4 at a=2 and use it to approximate (1.3)^1/4
Solution:
L(x)=f(a)+f'(a)(x-a)
=1+1/4(x-2)
L(2.3)=1+1/4(2.3-2)
=1.075
I really don't understand why 2.3 would be substituted into the equation instead of 1.3....any explanation to this would be much appreciated!