Question

On an open interval (a,b), if the function f(x) has exactly one critical value, f¹(x) then has:

A) One critical point
B) Two critical points
C) No critical points
D) Infinitely many critical points

Answer 1

If the function f(x) has exactly one critical value on an open interval (a,b), then f¹(x) will have A. one critical point.

Step-by-step explanation:

In the given question, we are asked to determine the number of critical points of the function fⁿ(x) on an open interval (a,b), given that f(x) has exactly one critical value. A critical value of a function corresponds to a point where the derivative of the function is equal to zero or undefined.

If f(x) has exactly one critical value, then fⁿ(x) will have either one or zero critical points. This is because if the derivative of f(x) is zero at one point, it cannot be zero at any other point, as that would give rise to multiple critical values.

Therefore, the correct answer is A) One critical point.