Answer:
A (9, 3)
Step-by-step explanation:
First the point is rotated 90° counterclockwise about the origin. To do that transformation: (x, y) → (-y, x).
So S(-3, -5) becomes S'(5, -3).
Next, the point is translated +4 units in the x direction and +6 units in the y direction.
So S'(5, -3) becomes S"(9, 3).
Answer:
A) g is increasing, and the graph of g is concave up.
Step-by-step explanation:
g'(x) = ∫₀ˣ e^(-t³) dt
Since e^(-t³) is always positive, ∫₀ˣ e^(-t³) dt is positive when x > 0. So the function is increasing.
Find g"(x) by taking the derivative using second fundamental theorem of calculus:
g"(x) = e^(-x³)
g"(x) is always positive, so the function is always concave up.
