Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Finding an equation of a tangent line. A. find an equuation of the tangent line to the graph of f at the given point.
B. use a graphing utlity to graph the function and its tangent line to the point
C. use the derivative feature of the graphing utility to confirm your results.
the general form of a tangent line is (y-y1)=m(x-x1) where m is the slope and (x1,y1) are the coordinates
we have been given the function at (4,5)
to find the slope we will derivate the given function
putting the value of x we have
hence the slope is m=
the equation of a tangent line by putting the values of (x 1,y 1) =(4,5) is
in this graph blue line represents the tangent line and the graph f(x) is represented by the red line
We know that the tangent touches the graph at one point we can see from the graph that it touches at a point (4,5)
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Solved in 3 steps with 2 images
