Help!!! I don’t understand how to do this

Mathematics

1 answer:

lidiya [134]4 years ago

4 0

Answer:

$f^{(k)}(x)=\dfrac{17k!(-1)^k}{(x-9)^{k+1}}$

Step-by-step explanation:

The question presumes you have access to a computer algebra system. The one I have access to provided the output in the attachment. The list at the bottom is the list of the first four derivatives of f(x).

The derivatives alternate signs, so (-1)^k will be a factor.

The numerators start at 17 and increase by increasing factors: 2, 3, 4, indicating k! will be a factor.

The denominators have a degree that is k+1.

Putting these observations together, we can write an expression for the k-th derivative of f(x):

$\boxed{f^{(k)}(x)=\dfrac{17k!(-1)^k}{(x-9)^{k+1}}}$

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A more readable version of the question is:
Maria is on a hike. If she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike.

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