Question

the function ( f(x)=2 x^{3}-21 x^{2}+60 x - 3 ) has two critical values. the smaller one equals (square) and the larger one equals (square)

Explanation:

Step1: Find the derivative of the function

The derivative of \(f(x)=2x^{3}-21x^{2}+60x - 3\) is \(f^\prime(x)=6x^{2}-42x + 60\).

Step2: Set the derivative equal to zero

Set \(6x^{2}-42x + 60 = 0\). Divide through by \(6\) to get \(x^{2}-7x + 10=0\).

Step3: Factor the quadratic equation

Factor \(x^{2}-7x + 10=(x - 2)(x - 5)=0\).

Answer:

The smaller critical value is \(2\) and the larger critical value is \(5\).