Answer:
[tex] g(x) = \sqrt[3]{x-1} - 2 [/tex]
Step-by-step explanation:
We want to find h and k in:
[tex] g(x) = \sqrt[3]{x-h} + k [/tex]
At the inflection point, the second derivative is equal to zero, so:
[tex] g'(x) = \frac{1}{3} (x-h)^{\frac{-2}{3}} [/tex]
[tex] g''(x) = \frac{1}{3} \frac{-2}{3}(x-h)^{\frac{-5}{3}} = 0 [/tex]
Then x - h = 0.
Inflection point is located at (1, -2), replacing this x value we get:
1 - h = 0
h = 1
We know that the point (-2.5, -3.5) belongs to the function, so:
[tex] -3.5 = \sqrt[3]{-2.5-1} + k [/tex]
k ≈ -2
All data, used or not, are shown in the picture attached.
