10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
1 answer:
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.
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Answer:
Multiply by ∛2 and translate the graph to left by 4 units.
Step-by-step explanation:
The initial function given is:
y = -∛(x - 4)
The transformed function is:
y = -∛(2x - 4)
Consider the initial function.
y = -∛(x - 4)
(Represented by Black line in the graph)
Multiply the function by ∛2. The function becomes:
y = -∛(x - 4) × ∛2
y = -∛(2)(x-4)
y = -∛(2x-8)
(Represented by Red line in the graph represents this function)
Translate the graph 4 units to the left by adding 4 to the x component:
y = -∛(2x-8+4)
y= -∛(2x - 4)
(Represented by Blue line in the graph)
