Question

the function $f(x)=2x^{3}-18x^{2}+30x - 5$ has two critical values. the smaller one equals and the larger one equals

Explanation:

Step1: Find the derivative of f(x)

$f(x)=2x^{3}-18x^{2}+30x - 5$, so $f^\prime(x)=6x^{2}-36x + 30$

Step2: Set the derivative equal to zero

$6x^{2}-36x + 30 = 0$. Divide through by 6: $x^{2}-6x + 5=0$

Step3: Factor the quadratic equation

$(x - 1)(x - 5)=0$

Step4: Solve for x

$x-1=0$ gives $x = 1$; $x - 5=0$ gives $x = 5$

Answer:

The smaller one equals 1 and the larger one equals 5.