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2 years ago

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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victus00 [196]

Answer:

a. The critcal points are at

$x=0,-5,3$

b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

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(a)

Remember that you need to find the points where

$f'(x)=0$

Therefore you have to solve this equation.

$20x^4 + 40x^3 - 300x^2 = 0$

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