Question 42: Which of the following graphs of functions has (3) extreme points.

Question 42: Which of the following graphs of functions has \(3\) extreme points.

A. \(y = – {x^4} – 2{x^2} – 1\)

B. \(y = {x^4} + 2{x^2} – 1\)

C. \(y = 2{x^4} + 4{x^2} + 1\)

D. \(y = {x^4} – 2{x^2} – 1\)

Note that the function \(y = a{x^4} + b{x^2} + c\left( {a \ne 0} \right)\) has three extremes when \( – \frac{b} {a} > 0\).

The function \(y = {x^4} – 2{x^2} – 1\) has \( – \frac{b}{a} = – \frac{{ – 2}}{1} = 2 > 0\).

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