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

$f(x)=\frac{2}{(x^2-4x)^2}$

Find out the first derivative

$f^{\prime}(x)=-\frac{4(2x-4)}{(x^2-4x)^3}$

Evaluate at (5,2/25)

so

For x=5

substitute in the first derivative

$f^{\prime}(5)=-\frac{4(2(5)-4)}{(5^2-4(5))^3}$$f^{\prime}(5)=-\frac{4(6)}{(5)^3}$$f^{\prime}(5)=-\frac{24}{125}$

therefore

f'(5)=-0.192