Question

when finding the tangent of a function with only one given point....do i draw a secant line? and find the limit?

Answer 1

is the point given the point of tangency?

Answer 2

If you have the function and the point of tangency, use point slope form of a line and substitute the point and first derivative evaluated at that point for the slope and you are good to go....

Answer 3

you need two point for a secant line. let say (c, f(c) ) and (c+h, f(c+h)) . you get the derivative of the function by try to make h -> 0 . \[\lim_{h \rightarrow 0} [f(x+h)-f(x)]/h\] . that's m. input it to y-y1=m(x-x1) you get the tangent line

Answer 4

The question stated, "when finding the tangent of a function with only one given point....do i draw a secant line? and find the limit?"

Only one point is needed if the one point is the point of tangency!!
This is the case because the evaluation of the derivative of the function at that point represents the slope of the tangent line at that point. Using the x and y coordinates you can then use the point-slope form of the line....you are done.....

If the pont given is not a point of tangency the process is quite different.

Answer 5

If the point is "not" the point of tangency, you still only need ONE point...but a little more work....First...take the derivative of the given function and allow that to represent your slope of the tangent line. then substitute that value along with the given point into the point slope form of a line. You then need to find the intersection of the given function and the one you just generated. Using this point you not can find the value of the slope of the tangent line and then using either point the equation of the tangent line. A nice example would be to use y=x^3-x and the point (0,4). It works nicely.