For a given value, the approximate value the function approaches for that value is called as the Linear
approximation. Linear approximation is calculated by the linear approximation formulaf(x) = f(x0) + f'(x0) (x –
x0). The online tool used to calculate the linear approximation using the linear approximation formula is called
as linear approximation calculator.
Example 1: Find the linear approximation f(x) = 3x2 when x tends to 4.
Given f(x) = 3x2 and the x approaches 4;
x0 = 4; f(4) = 3 * 42 = 48.
f'(x) = 6x <- f'(4) = 6*4 = 24.
Linear approximation formula f(x) = f(x0) + f'(x0) (x –x0)
f(x) = 48 + 24(x - 4)
f(x) = 48 + 24x - 96
f(x) = 24 x - 48.
Liner approximation of f(x) = 24 x - 48.
Example 2: Find the linear approximation f(x) = 2x + 1 when x tends to 3
Given f(x) = 2 x + 1 and the x approaches 3.
<-x0 = 3 <-f(3) = 2*3 + 1 = 7.
<-f'(x) = 2<- f'(3) = 2.
Linear approximation formulaf(x) = f(x0) + f'(x0) (x –x0)
<-f(x) = 7 + 2(x - 3)
<-f(x) = 7 + 2 x - 6;
f(x) = 2x + 1
Liner approximation of f(x) = 2x + 1.