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Response Details:
Hi,
Remember, whenever you say, "the instantaneous rate of change" that means you will be taking the derivative of the given function.
In this example, you will be using the Power Rule on each individual part of the given function. Here's what the rule says:
You need to remember this rule as it comes back in Calc II. 
Your First Example:
Remember the rule . . .
I want you to notice the process that I've outlined. The green represents the bringing down of the power. I then used red to subtract 1 from the power to make it degree 1.
However, you wanted the instantaneous slope at x = 5, therefore:
f ' ( x ) = x
Then . . . f ' (5) = 5
Second Example:
f ( x ) = x2 + 3x - 11
Recall the rule: Derivative of x2 is always 2x.
Now, recall, what is the slope of the graph which is y = 3x ? I'm sure you would say 3 which is indeed the derivative.
Next, if I showed you the graph of y = 11 (a horizontal line) I'm sure you would say that it has no slope or 0.
The rule applies just like in the previous example:
Now, you wanted the rate of change at x = 2, so therefore we say:
f ' (x) = 2x + 3
f ' (x) = 2(2) + 3
f ' (x) = 4 + 3
f ' (x) = 7
I hope that helps you out! Please let me know if you have any other questions!
Sincerely,
Andrew
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