A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema...

Question

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x^4 - 16x^3 + 24x^2 - 37a is:

A. 0
B. 1
C. 2
D. 3

Accepted Answer

B. 1 An extremum (local max or min) occurs where f'(x) = 0 AND f''(x) != 0 (second derivative test). We find all critical points by solving f'(x) = 0, then check the second derivative at each. Points where f'(x) = 0 but f''(x) = 0 might be inflection points, not extrema.

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x^4 - 16x^3 + 24x^2 - 37a is: A. 0 B. 1 C. 2 D. 3