Answer to Question #269901 in Calculus for nikki

Question

 A differentiable function f has the property that f(5)=3

f′(5)=4 Whats the estimate for f(4.8) using the local linear approximation for f at x= 5 ?

Answer 1

We know that, f(x+δx)≈f(x)+f'(x)⋅δx.........(⋆)

Letting, x=5,and,x+δx=4.8⇒δx=−0.2 in (⋆), we get,

f(5−0.2)=f(4.8)≈f(5)+f'(5)(−0.2),

=4−3(−0.2)=4−0.6

Therefore, f(4.8)≈3.4