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Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
Find the equation of a tangent line?
find the derivative to get the slope, then using the graph of the other line given to you, find a point on the graph that they share and plug it in to find the y-value. then use the point slope formulahttp://docs.google.com/gview?a=v&q=cache:P72siWJTFjwJ:gato-docs.its.txstate.edu/slac/Subject/Math/Calculus/Findting-the-Equation-of-a-Tangent-Line/Finding%2520the%2520Equation%2520of%2520a%2520Tangent%2520Line.pdf+how+to+find+the+equation+of+a+tangent+line&hl=en&gl=us&sig=AFQjCNFcYzt1d-PU9hE2gbQKngp4FeRw3Q
Find the equation of the tangent line at the given value y equals ln x squared at x equals 1?
Given y=LN(x2). To find the equation of a tangent line to a point on a graph, we must figure out what the slope is at that exact point. We must take the derivitave with respect to x to come up with a function that will give the slope of the tangent line at any point on the graph. Any text book will tell you that the derivative with respect to X of LN(U) is the quantity U prime over U(In other words, the derivitive of U over U. U is whatever is inside the natural log). In this case, it is y = (2x/x2). To find the slope, we then plug in an x coordinate, 1. We get y=2. The slope of the tangent line at this point is 2. We now have m for the slope-intercept form y = mx + b. Now we must find b. B is the y intercept, aka where does the graph intersect the y axis. We use the slope. We know that the graph of the tangent line contains the point (0,1). We go down 2 and left one, to find that the tangent line intercepts the y axis at -1. We now have B. The equation of the tangent line of y = LN(x2) at X = 1 is y = 2X-1. Hope this helps!!!
Is the steepness of a line on a motion graph is called a slope?
"Slope" is the steepness of the line on any graph.
How do you tell whether a graph shows a constant or variable rate of change?
The slope of each point on the line on the graph is the rate of change at that point. If the graph is a straight line, then its slope is constant. If the graph is a curved line, then its slope changes.
