Consider the graph of f(x) = 5x 6 – 5x 5 – x 4.

On a coordinate plane, a graph decreases through (negative 0.6, 0.4), has an inflection point (0, 0), decreases through (0.5, negative 0.2) to (1, negative 1), and then increases up through (1.2, 0).

Based on the graph, what is the solution to
5x6 – x4 > 5x 5?

One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than x less-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than-or-equal-to x less-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
x less-than one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
x less-than-or-equal-to one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

The other person said B, but it's not because it can't be equal to either. X is between .17 and 1.17, but cannot equal. I got this by putting it into des.mos and getting the graphs

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-01-13T14:35:29+01:00

Inequalities are used to represent unequal expressions

The solution to [tex]5x^6 - x^4 > 5x^5[/tex] is [tex]\frac 12 - \frac 3{10} \sqrt 5< x <\frac 12 + \frac 3{10} \sqrt 5[/tex]

The equation and Inequality

The equation of the function is given as:

[tex]f(x) = 5x^6 - 5x^5 - x^4[/tex]

The inequality is then given as:

[tex]5x^6 - x^4 > 5x^5[/tex]

Graph

See attachment for the graph of the inequality

From the attached graph, we can see that the inequality crosses the x-axis at:

[tex]x = -0.17\ and\ x = 1.17[/tex]

These values can be represented as:

[tex]\frac 12 - \frac 3{10} \sqrt 5< x <\frac 12 + \frac 3{10} \sqrt 5[/tex]

Hence, the solution to [tex]5x^6 - x^4 > 5x^5[/tex] is [tex]\frac 12 - \frac 3{10} \sqrt 5< x <\frac 12 + \frac 3{10} \sqrt 5[/tex]