Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Mark the correct alternative of the following. The least and greatest values of
Mark the correct alternative of the following. The least and greatest values of \( f(x)= \) \( x^{3}-6 x^{2}+9 x \) in \( [0,6], \) are?
- A. 3,4
- B. 0,6
- C. 0,3
- D. 3,6
Step-by-step solution
Find critical points by derivative: f'(x)=3x^2-12x+9=3(x-1)(x-3). Critical points at x=1 and x=3. Evaluate f at endpoints and critical points: f(0)=0, f(1)=4, f(3)=0, f(6)=54. The least value is 0 at x=0 and x=3; the greatest value is 54 at x=6. The question likely asks for the x-coordinates of the least and greatest values, which are 0 and 6 respectively.
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