High School

Compute the formula for the line that is tangent to the function [tex]f(x) = -3(x+1)^2 + 2[/tex] at [tex]x = 3[/tex].

A. [tex]y = -24x + 26[/tex]
B. [tex]y = -24x - 46[/tex]
C. [tex]y = 24x + 26[/tex]
D. [tex]y = 24x + 46[/tex]
E. [tex]y = 24x[/tex]
F. None of the above

Answer :

Final answer:

Explaining how to calculate the formula for the tangent line to a function and determining the correct answer for the given question is y=−24x+26 . The correct option is A .

Explanation:

The formula for the line that is tangent to the function f(x) = −3(x+1)²+2 at x=3 can be computed using the derivative of the function.

To find the equation, follow these steps:

  1. Calculate the derivative of the function f(x).
  2. Substitute x=3 into the derivative to find the slope at x=3.
  3. Use the slope and the point (3, f(3)) to determine the equation of the tangent line using the point-slope form of a line equation.

The tangent line to the function f(x) = -3(x+1)2 + 2 at x = 3 is found by calculating the derivative, determining the slope at x = 3, and then using the point-slope form of a line; the correct equation is y = -24x + 74, The correct formula for the tangent line is y = -24x + 26 (option a).

Other Questions