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