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.

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)

Now we equate the derivative to 0.

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

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

536

step-by-step explanation:

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: