Answered

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Find the domain over which the function y = x + 6x is monotonic increasing.

Sagot :

semsee45

Answer:

x > -3

[tex]\sf (-3, \infty)[/tex]

Step-by-step explanation:

Domain: input values (x-values)

Monotonic increasing:  always increasing.  
A function is increasing when its graph rises from left to right.

The graph of a quadratic function is a parabola.  If the leading term is positive, the parabola opens upwards.  The domain over which the function is increasing for a parabola that opens upwards is values greater than the x-value of the vertex.

Vertex

Standard form of quadratic equation:  [tex]\sf y=ax^2+bx+c[/tex]

[tex]\textsf{x-value of vertex}=\sf -\dfrac{b}{2a}[/tex]

Given function:

[tex]\sf y=x^2+6x[/tex]

Therefore, x-value of function's vertex:

[tex]\sf \implies x= -\dfrac{6}{2}=-3[/tex]

Final Solution

The function is increasing when x > -3

[tex]\sf (-3, \infty)[/tex]

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