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