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Rate of change as x goes from -infinity to infinity for y = 3x³.

a) Increases
b) Decreases
c) Remains constant

User SridharS
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1 Answer

2 votes

Final answer:

The rate of change of the function y = 3x³ increases as x goes from -infinity to infinity because the derivative, 9x², is always positive for x other than zero.

Step-by-step explanation:

The function given is y = 3x³. To determine the rate of change as x goes from -infinity to infinity, we can examine the derivative of the function, since the derivative represents the rate of change of the function with respect to x. The derivative of y = 3x³ is dy/dx = 9x². Since 9x² is always positive for all x except at x = 0 where it is zero, the rate of change of the function is always positive. This means as x increases from -infinity to infinity, the function's rate of change also increases.

Therefore, the correct answer to the student's question is (a) Increases.

User Ben McNiel
by
7.5k points

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