Question

question 22 of 25
what is the maximum number of relative extrema contained in the graph of
this function?

$f(x) = 3x^5 - x^3 + 4x - 2$

Explanation:

Step1: Find derivative of f(x)

$f'(x) = 15x^4 - 3x^2 + 4$

Step2: Analyze derivative's roots

Let $y = x^2$, then $f'(x) = 15y^2 - 3y + 4$. Discriminant: $\Delta = (-3)^2 - 4(15)(4) = 9 - 240 = -231 < 0$

Step3: Determine extrema existence

Since discriminant is negative, $f'(x)$ has no real roots. Thus, no relative extrema.

Answer:

0