Mathematics: In your lab, a substance s temperature has been observed to follow the function f(x) = (x − 1)3 + 9. the point at which the function changes curvature from concave down to concave up is where the substance changes from a solid to a liquid. what is the point where this function changes curvature from concave down to concave up? hint: the point is labeled in the picture.

4.2 times 100000Step-by-step explanation:...

In your lab, a substance s temperature has been observed

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10.03.2022

The point of change is the point (1,9)

Step-by-step explanation:

The first derivative of the function equated to zero will give you the point where the function changes.

Therefore, to solve this problem find the first derivative of f (x)

$f '(x) = 3*3(x-1)^{3-1}\\\\f '(x) = 9(x-1)^2$

Now we equate the derivative to 0.

$9 (x-1)^ 2 = 0\\\\x = 1$

Then the derivative of the function is equal to 0 when x = 1. This means that the concavity of the function changes in x = 1.

When $x = 1, y = 3(1-1) ^ 3 +9\\\\x =1, y = 9.$

Then the point of change is the point (1,9)

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