Question

given the function below

f(x)=sqrt3{-50 x^{3}+175}

find the equation of the tangent line to the graph of the function at ( x = 1 ). answer in ( m x + b ) form.

use the tangent line to approximate ( f(1.1) ).

compute the actual value of ( f(1.1) ). what is the error between the function value and the linear approximation?
answer as a positive value only.

question help: video message instructor

Explanation:

Step1: Calculate \(f(1.1)\)

Substitute \(x = 1.1\) into \(f(x)=\sqrt[3]{-50x^{3}+175}\)

$$
LATEXBLOCK0
$$

Step2: Calculate the error

The error \(E=\vert f(1.1)-L(1.1)\vert\). We know \(L(1.1) = 4.8\)

$$
LATEXBLOCK1
$$

Answer:

\(0.03203\)