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A) The signs of the first derivative (g') tell you the graph increases as you go left from x=4 and as you go right from x=-2. Since g(4) < g(-2), one absolute extreme is (4, g(4)) = (4, 1).
The sign of the first derivative changes at x=0, at which point the slope is undefined (the curve is vertical). The curve approaches +∞ at x=0 both from the left and from the right, so the other absolute extreme is (0, +∞).
b) The second derivative (g'') changes sign at x=2, so there is a point of inflection there.
c) There is a vertical asymptote at x=0 and a flat spot at x=2. The curve goes through the points (-2, 5) and (4, 1), is increasing to the left of x=0 and non-increasing to the right of x=0. The curve is concave upward on [-2, 0) and (0, 2) and concave downward on (2, 4]. A possible graph is shown, along with the first and second derivatives.
The sign of the first derivative changes at x=0, at which point the slope is undefined (the curve is vertical). The curve approaches +∞ at x=0 both from the left and from the right, so the other absolute extreme is (0, +∞).
b) The second derivative (g'') changes sign at x=2, so there is a point of inflection there.
c) There is a vertical asymptote at x=0 and a flat spot at x=2. The curve goes through the points (-2, 5) and (4, 1), is increasing to the left of x=0 and non-increasing to the right of x=0. The curve is concave upward on [-2, 0) and (0, 2) and concave downward on (2, 4]. A possible graph is shown, along with the first and second derivatives.
d = log₂p represents a logarithmic function, The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.
<h3>What is an exponential function?</h3>An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let p represent the bacteria population in thousand after d days.
Since each day, the bacteria population grows by a factor of 2, hence:
Hence, d = log₂p represents a logarithmic function
The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.
Find out more on exponential function at: brainly.com/question/12940982