# How do you find the linearization of #f(x)=4x^3-5x-1# at a=2?

Find the equation of the tangent line at the point

The equation of the tangent line (in point-slope form) is

The linearization is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the linearization of ( f(x) = 4x^3 - 5x - 1 ) at ( a = 2 ), follow these steps:

- Find the value of ( f(a) ) at ( a = 2 ) by substituting ( x = 2 ) into the function ( f(x) ).
- Find the derivative ( f'(x) ) of the function ( f(x) ).
- Evaluate ( f'(a) ) at ( a = 2 ) to find the slope of the tangent line at ( x = 2 ).
- Use the point-slope form of a linear equation ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is the point ( (2, f(2)) ) and ( m ) is the slope ( f'(2) ), to write the equation of the tangent line.

By following these steps, you can find the linearization of ( f(x) ) at ( a = 2 ).

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find two numbers whose difference is 100 and whose product is a maximum?
- What are the coordinates of the points a and b and minimize the length of the hypotenuse of a right triangle that is formed in the first quadrant by the x-axis, the y-axis, and a line through the point (1,2) where point a is at (0,y) and point b is at (x,0)?
- Demand for rooms, of a hotel which has #58# rooms, is a function of price charged given by #u(p)=p^2-12p+45#. Find out at what price the revenue is maximized and what is the revenue?
- If a ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second, for how long will the ball be going upward?
- How do you use linear approximation to the square root function to estimate square roots #sqrt 3.60#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7