Calculus :

I need the whole page, including discussion 1 and 2 at the bottom answered. Please show work if possible and put a box on the final answer so it is easy to follow:

a) Find the derivative. b) Evaluate f ' (1) c] Evaluate f (1) d) Draw the tangent line at x = 1 Write the equation of the tangent line to the function at x = 1 3]: Compare the y-value for the tangent line at x = 1.1 to the y-value of the original function at x = 1.1 Original function, f (1.1) x Tangent line, L(1.1) z Discussion 1: The tangent line equation to a function a certain point is called the linearization of that function at Q. Why do you think it's called the linearization? [Answer one sentence) Discussion 2: The linearization of a function at a point is often used to approximate values of the function near that point. Why do you think someone would want to do this? [Answer one sentence)