Question

If the graph of f(x) = ax³ - bx² + cx - d has a local maximum at (0, 6) and a local minimum at (2, −2), compute the value of f(1).

a) 1
b) 2
c) 3
d) 4

Answer 1

To compute the value of f(1), we need to find the value of the function f(x) at x = 1.

Step-by-step explanation:

To compute the value of f(1), we need to find the value of the function f(x) at x = 1. Since we know that the graph has a local maximum at (0, 6) and a local minimum at (2, -2), we can define the function f(x) as follows:

f(x) = ax³ - bx² + cx - d

Using the given points, we can substitute them into the function to form a system of equations:

f(0) = 6 = a(0)³ - b(0)² + c(0) - d

f(2) = -2 = a(2)³ - b(2)² + c(2) - d

Solving this system of equations will allow us to find the values of a, b, c, and d. Once we have those values, we can determine the value of f(1).