5 true or false 1 point the range of the graph of this equation is 1.8974, ∞). y = x^4 - 4x^3 + 14/3 x^2…

5 true or false 1 point the range of the graph of this equation is 1.8974, ∞). y = x^4 - 4x^3 + 14/3 x^2 - 9/7 x + 2 true false

5 true or false 1 point the range of the graph of this equation is 1.8974, ∞). y = x^4 - 4x^3 + 14/3 x^2 - 9/7 x + 2 true false

Answer

Explanation:

Step1: Find the derivative

Differentiate $y = x^{4}-4x^{3}+\frac{14}{3}x^{2}-\frac{9}{7}x + 2$ using the power - rule. $y'=4x^{3}-12x^{2}+\frac{28}{3}x-\frac{9}{7}$.

Step2: Find critical points

Set $y' = 0$ and solve for $x$. This is a cubic equation. We can use a graphing utility or numerical methods (e.g., Newton - Raphson method). Another way is to analyze the behavior of the function. Since the leading coefficient of $y$ (the coefficient of $x^{4}$) is positive ($a = 1>0$), the function is a parabola - like shape opening upwards. We can also use a graphing calculator or software (e.g., Desmos) to graph the function $y = x^{4}-4x^{3}+\frac{14}{3}x^{2}-\frac{9}{7}x + 2$. By graphing the function, we find that the minimum value of the function is approximately $1.8974$.

Answer:

True