Posted by art on Friday, February 11, 2011 at 11:02pm.
f(x)=35x , (1,8) find the slope of the tangent line to the graph of the function at the given point
how do you figure this out?

calculus  Reiny, Friday, February 11, 2011 at 11:07pm
since your function is a straight line
and it is in the form f(x) = mx + b
the slope anywhere on the line is 5
no work needed here.

calculus  Allison, Friday, February 11, 2011 at 11:09pm
To find the slope of the tangent line you have to take the first derivative of f(x). So f'(x)=5. Or you can also see that from the formula y=mx+b, where m is slope and b is your y intercept, that 5 is the slope. Because the original function is a line, the slope is the same at every point.

calculus  helper, Friday, February 11, 2011 at 11:10pm
To find the slope of the tangent line at a point means to find the derivative of f(x).
f(x) = 3  5x
f' = 0  5
f' = 5
Then, normally, you would plug in the given point, (1, 8), to find the slope.
But since f' = 5 with no variable x, for instance, there is nowhere to plug in the point.
Therefore, the slope is everywhere.
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