Question

Найдите промежутки возрастания и убывания функции

Answer 1

$y=-3x+e^{3x}\\\\y'=-3+3e^{3x}=3(e^{3x}-1)=0\\\\e^{3x}=1\; \; \to \; \; 3x=0\; ,\; \; x=0\\\\-----(0)+++++\\\\vozrastaet\; na\; \; (0,+\infty )\\\\ybuvaet\; na\; \; (-\infty ,0)$

Answer 2

Finding the Intervals of Increase and Decrease for a Function

To find the intervals of increase and decrease for a function, we need to analyze the sign of the derivative of the function. When the derivative is positive, the function is increasing, and when the derivative is negative, the function is decreasing.

Unfortunately, the search results provided do not include specific functions or equations to analyze. However, I can provide a general explanation of how to find the intervals of increase and decrease for a function.

1. Find the derivative of the function. 2. Set the derivative equal to zero and solve for x to find the critical points. 3. Create a sign chart by selecting test points from each interval between the critical points. 4. Determine the sign of the derivative in each interval. 5. If the derivative is positive, the function is increasing in that interval. If the derivative is negative, the function is decreasing in that interval.

Please provide the specific function or equation you would like me to analyze, and I will be happy to help you find the intervals of increase and decrease.