Elizabeth bought a plant and planted it in a pot near a window in her house. Let H represent the height of the plant, in inches,
t months since Elizabeth bought the plant. The table below has select values showing the linear relationship between t and H. Determine the height of the plant 9.5 months after being planted. (See SS attached)
2 answers:
You might be interested in
The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so