Tutor profile: Justin L.
How do you find the domain of a square root function?
To find the domain of a square root function, set everything inside the square root greater than or equal to 0 and solve for x. This is because we can never have a negative inside a square root, so we need to find what values of x result in 0 or larger inside.
What quadrants is sine positive and negative? What about cosine? What about tangent?
Sine is positive in quadrants I and II. This is because the y coordinates are positive in these quadrants. Cosine is positive in quadrants I and IV due to the x coordinates being positive in these quadrants. Tangent is positive in quadrant I and III. It is positive in quadrant I since both x and y coordinates are positive. It is positive in quadrant III because both x and y coordinates are negative and since tangent is y/x, the negatives cancel out.
Write out the steps to find intervals of increase/decrease and local extrema.
The first step would be to find critical points. To do this, find the derivative of the given function. Set it equal to 0 and solve for x. Any values you find AND any values that would make the first derivative undefined are critical points. To test for intervals of increase/decrease, set any critical points and vertical asypmtotes on a number line. Pick a "test point" from each interval. Substitute these test points into the first derivative. If a test point results in a positive result, then that entire interval is increasing. If a test point results in a negative result, then that entire interval is decreasing. A local minimum occurs where a function changes from decreasing to increasing. A local maximum occurs where a function changes from increasing to decreasing. A vertical asymptote is not a min/max, even if the function follows these patterns at a vertical asymptote.
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