Slope of Horizontal tangent line
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Harry_the_cat
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A horizontal tangent means the gradient is what?
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Harry_the_cat
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Ok so now write the points in the form (x, y) to answer the question.
Steven G
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It seems that you are saying that the answers are 4 and 0 and I do understand that you mean y=4 and y=0.
Stating the y values where you have horizontal tangent lines is not a good idea. The reason is that a graph can have many points on it where y=4 and many points where y=0 (just think of a graph that has many x-intercepts) but maybe (and probably!) not all of those points where y=0 and y=4 have horizontal tangent line. That is why it is better to state the x-values. Remember that for every x-value a function has only one y-value. So saying that the horizontal lines occur when x=1 and x=-1 is much better than stating the y-values.
Now there is still a problem when I say to just state the x-values x=1 and x=-1. The problem says to find the point(s) where you have horizontal tangent lines. As you know a point has an x and y value. As Harry_the_cat pointed out you need to write the points in (x,y) form to formally answer the question.
Stating the y values where you have horizontal tangent lines is not a good idea. The reason is that a graph can have many points on it where y=4 and many points where y=0 (just think of a graph that has many x-intercepts) but maybe (and probably!) not all of those points where y=0 and y=4 have horizontal tangent line. That is why it is better to state the x-values. Remember that for every x-value a function has only one y-value. So saying that the horizontal lines occur when x=1 and x=-1 is much better than stating the y-values.
Now there is still a problem when I say to just state the x-values x=1 and x=-1. The problem says to find the point(s) where you have horizontal tangent lines. As you know a point has an x and y value. As Harry_the_cat pointed out you need to write the points in (x,y) form to formally answer the question.