How do you find the slope of a tangent line to the graph of the function #F(t)= 3- (8/3t)# at point: (2/4, -7/3)?

Question

Scarlett Allison · Accepted Answer

There is no such line.

The point #(2/4,-7/3)# is not on the graph of that function. But at any point #(a/b)# that is on the graph, the slope of the tangent line is the same as the slope of the line. So it is #-8/3#

Charles Anctil · Answer

undefined To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. In this case, the function is F(t) = 3 - (8/3t), and the point of interest is (2/4, -7/3).

To find the derivative of F(t), you can use the power rule and the constant rule. The derivative of 3 is 0, and the derivative of -(8/3t) is -(8/3) * (1/t^2), which simplifies to -8/(3t^2).

Now, substitute the x-coordinate of the given point (2/4) into the derivative expression to find the slope at that point. The slope of the tangent line is -8/(3 * (2/4)^2), which simplifies to -8/(3 * 1/4), and further simplifies to -32.

Therefore, the slope of the tangent line to the graph of F(t) = 3 - (8/3t) at the point (2/4, -7/3) is -32.