`f(t) = 2 - 4/t,. (4,1)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

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kalau | (Level 2) Adjunct Educator

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Rewrite the given function so that we can proceed with the power rule instead of the quotient rule.

`f(t)=2-4t^(-1)`

Take the derivative of the given function.  The derivative of a constant is zero.

`f'(t) = 4t^(-2) = 4/t^2`

Substitute `(t,f(t)) = (4,1)` .

`f'(4)=4/(4^2) = 4/16 = 1/4`

The derivative, or the slope, at the point is one-fourth.

Graph the derivative function and check the value at t=4. It appears to be about 1/4.