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

User Pedro Rio
by
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1 Answer

11 votes

Answer:

x > -3


\sf (-3, \infty)

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:
\sf y=ax^2+bx+c


\textsf{x-value of vertex}=\sf -(b)/(2a)

Given function:


\sf y=x^2+6x

Therefore, x-value of function's vertex:


\sf \implies x= -(6)/(2)=-3

Final Solution

The function is increasing when x > -3


\sf (-3, \infty)

User Dick Goodwin
by
7.3k points