Question

For the function y= -(x ³) ²−5,, the graph exhibits a:

A) Maximum
B) Minimum
C) Neither maximum nor minimum
D) Both maximum and minimum

Answer 1

The function y = -(x^3)^2 - 5 simplifies to y = -x^6 - 5 and has a graph that exhibits a minimum because it opens downwards and is bounded by -5.

Step-by-step explanation:

The student has asked about the function y = -(x^3)^2 - 5 and its graph characteristics. This function can be simplified to y = -x^6 - 5. To determine whether the graph of this function exhibits a maximum, minimum, or neither, we can look at the leading term, which is -x^6.

The negative coefficient of the leading term and the even exponent indicate that the graph will open downwards and have no maximum value, but it will have a minimum value since the function can approach negative infinity but is bounded by the constant -5. Therefore, the graph of this function exhibits a minimum.