At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)
Practice Questions
1 question
Q1
At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)
(1, 2)
(2, 1)
(0, 4)
(3, 0)
To find local minima, we find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Checking the second derivative, f''(2) = 6 > 0, so (2, 1) is a local minimum.
Questions & Step-by-step Solutions
1 item
Q
Q: At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)
Solution: To find local minima, we find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Checking the second derivative, f''(2) = 6 > 0, so (2, 1) is a local minimum.
