question 20 of 25\nwhat is the maximum number of relative extrema contained in the graph of this…
question 20 of 25\nwhat is the maximum number of relative extrema contained in the graph of this function?\n$f(x)=3x^{4}-x^{2}+4x - 2$
Answer
Explanation:
Step1: Find the derivative of the function
The derivative of (f(x)=3x^{4}-x^{2}+4x - 2) is (f^\prime(x)=12x^{3}-2x + 4) (using the power rule ((x^n)^\prime=nx^{n - 1})).
Step2: Recall the relationship between degree of derivative and number of relative extrema
The number of relative extrema of a function (y = f(x)) is at most one less than the degree of the function. The degree of (f(x)) is (n = 4).
Answer:
(3)