The maximum number of relative extrema of the given polynomial is; 3
<h3>How to find the maxima of a Polynomial Function?</h3>
When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;
Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.
We are given the Polynomial as;
f(x) = 3x⁴ - x² + 4x - 2
Now, the degree of the Polynomial would be 4. Thus;
Maximum number of relative extrema = 4 - 1
Maximum number of relative extrema = 3
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Answer:
Slope = 300/2x = 150x
Equation: y = 150x
Step-by-step explanation:
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
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Answer:What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)2 + 4? ... Which best describes the transformation from the graph of f(x) = x2 to the graph of ... The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2. ... Which statement about the function is true?
Step-by-step explanation: