Question

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. (If an answer is undefined, enter UNDEFINED. Round your answer to three decimal places.)

Answer 1

we have the function

`f(x)=(2)/((x^2-4x)^2)`

Find out the first derivative

`f^(\prime)(x)=-(4(2x-4))/((x^2-4x)^3)`

Evaluate at (5,2/25)

so

For x=5

substitute in the first derivative

`f^(\prime)(5)=-(4(2(5)-4))/((5^2-4(5))^3)`
`f^(\prime)(5)=-(4(6))/((5)^3)`
`f^(\prime)(5)=-(24)/(125)`

therefore

f'(5)=-0.192