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romanna [79]
2 years ago
12

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

Mathematics
1 answer:
iragen [17]2 years ago
4 0

Answer:

x > -3

\sf (-3, \infty)

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.

<u>Vertex</u>

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

\textsf{x-value of vertex}=\sf -\dfrac{b}{2a}

Given function:

\sf y=x^2+6x

Therefore, x-value of function's vertex:

\sf \implies x= -\dfrac{6}{2}=-3

<u>Final Solution</u>

The function is increasing when x > -3

\sf (-3, \infty)

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