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How do you find the instantaneous rate of change of #y=5x+9# at x=2?

Answer 1

#y = 5x + 9# is a line in the form of #y = mx + b#

This means that the slope #m# at any point will the the same value, in this case, #5#. (Lines have constants slopes or rates of change.)

Using derivatives, we find that the #y' = 5# which confirms that the slope is #5# regardless of what the #x# value is. We only need to find the slope at a specific #x# value if the derivative has an #x# term in it.

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Answer 2

Cameron Alexander

To find the instantaneous rate of change of the function ( y = 5x + 9 ) at ( x = 2 ), you can find the derivative of the function with respect to ( x ), which represents the rate of change of ( y ) with respect to ( x ). Then, evaluate the derivative at ( x = 2 ) to obtain the instantaneous rate of change.
Taking the derivative of ( y = 5x + 9 ) with respect to ( x ) yields ( \frac{dy}{dx} = 5 ).
Evaluating ( \frac{dy}{dx} ) at ( x = 2 ) gives the instantaneous rate of change at that point, which is ( 5 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.