answer:To find the interval where the function y=xe^{x} is strictly increasing, we need to find the first derivative and determine where it is positive. The first derivative of y=xe^{x} is given by the product rule: y' = (x)'cdot e^{x} + x cdot (e^{x})' = e^{x} + xe^{x} Now, let's find where y' > 0: e^{x} + xe^{x} > 0 Factor out e^{x} (note that e^{x} > 0 for all x): e^{x}(1 + x) > 0 Since e^{x} > 0, the sign of y' only depends on (1 + x): 1 + x > 0 x > -1 Thus, the function y=xe^{x} is strictly increasing on the interval boxed{left( -1,+infty right)}.

answer:Given the inequality ax-b > 0 has a solution set of left(-infty, -1right), we can deduce certain properties about the coefficients a and b. 1. Since the solution set is left(-infty, -1right), it means for x < -1, ax - b > 0. This implies that as x becomes more negative (less than -1), the expression ax - b remains positive, suggesting that a < 0 (since a positive a would make ax - b negative for sufficiently negative x). 2. Given the boundary of the solution set is at x = -1, substituting x = -1 into the inequality gives us a(-1) - b = -a - b > 0, which simplifies to -a - b = 0. Therefore, we have b = -a. With these two pieces of information, we can rewrite the second inequality ax^2 + bx > 0 using b = -a: [ax^2 + bx > 0 Rightarrow ax^2 - ax > 0 Rightarrow a(x^2 - x) > 0] Since we know a < 0, we can divide both sides of the inequality by a (remembering to flip the inequality sign because a is negative): [x^2 - x < 0] Factoring the left side gives us: [x(x - 1) < 0] This inequality tells us that the product of x and (x - 1) is negative, which means one of them must be positive and the other negative. This situation occurs only between the roots of the equation x(x - 1) = 0, which are x = 0 and x = 1. Therefore, the solution set for x where the expression is negative (and thus the original inequality ax^2 + bx > 0 is satisfied) is between these two roots: [0 < x < 1] Thus, the solution set of the inequality ax^2 + bx > 0 with respect to x is boxed{(0,1)}. Therefore, the correct answer is: boxed{D}.

answer:The text is fairly coherent, but the use of the word “then” in the final sentence may not be strictly necessary and could be removed for improved cohesion.

answer:The doctor will use a special tube to open up your blocked blood vessel and help your heart get the blood it needs.