In mathematics, the tangent line to a curve at a point is a straight line that touches the curve at this point only. The tangent line can provide valuable insights into the properties of the curve, ...

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In math and statistics, you may occasionally need to calculate the slope of a line generated by coordinates in the (x,y) format. The slope is a value that indicates the rate at which the y value of a ...

Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...

Finding the slope of a linear function is straightforward. Furthermore the slope is the same at each point on the function. However this is not the case with non-linear functions. A non-linear ...

(a) \(f^\prime(1)=-7\text{;}\) (b) The slope equals to \(-7\text{;}\) (c) \(y=-7x+3\text{.}\) (a) See Figure 6.6.1.(b) Observe that all lines through \((3,1)\) are ...