Question

a. Write the equation of the line that represents the linear approximation to the following function at the given point a.

b. Use the linear approximation to estimate the given quantity.

c. compute the percent error in the approximation, 100* (|approximation-exact|)/|exact|, where the exact value is given by a calculator.

f(x)=15-3x^2 at a=2; f(1.9)

Answer 1

we are given

a=2

(A)

we can use formula

(B)

we can plug x=2

now, we can find derivative

now, we can plug x=2

now, we can plug these values

now, we can plug x=1.9

(c)

approximate =4.2

exact value:

now, we can find error

............Answer