To find the intervals of the function y = 2x^2 - 19x + 35, we need to determine where the function is increasing or decreasing.
Step 1: Find the critical points by setting the derivative equal to zero and solving for x.
The derivative of y = 2x^2 - 19x + 35 is dy/dx = 4x - 19.
Setting this equal to zero, we have 4x - 19 = 0.
Solving for x, we get x = 19/4 = 4.75.
Step 2: Determine the intervals using the critical point.
Since the critical point is x = 4.75, we can use a number line to determine the intervals.
Choosing a number less than 4.75, such as x = 0, we can evaluate the sign of the derivative.
dy/dx = 4(0) - 19 = -19. Since this is negative, the function is decreasing in the interval (-∞, 4.75).
Choosing a number greater than 4.75, such as x = 5, we can evaluate the sign of the derivative.
dy/dx = 4(5) - 19 = 1. Since this is positive, the function is increasing in the interval (4.75, ∞).
Therefore, the intervals of the function y = 2x^2 - 19x + 35 are (-∞, 4.75) and (4.75, ∞).
find the intervals of y=2x^2 - 19x+35
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