How can a linear approximation be used to approximate the value of a function f near a point at which f and f prime are easily evaluated?

This can be solved by calculating a first degree Taylor approximation polynomial for the function in question around x=a. Taylor's first degree polynomial is given by:

Through this expression, which is easily evaluable around the point x = a, the function f (x) is approximated through a linear function.

Step-by-step explanation:

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

14

step-by-step explanation:

14 x 3 = 42