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How do you find the average rate of change of #y=3x-2# over [x,x+h]?

Answer 1

Emma Aldridge

#3#

The average rate of change of the function #f(x)# over the interval #[a,b]# can be expressed as:

#"average rate of change"=(f(b)-f(a))/(b-a)#

So, for the function #f(x)=3x-2# and the interval #[x,x+h]#, this becomes:

#=(f(x+h)-f(x))/((x+h)-x)#

#=((3(x+h)-2)-(3x-2))/h#

#=(3x+3h-2-3x+2)/h#

#=(3h)/h#

#=3#

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Answer 2

Luke Alvarez

To find the average rate of change of the function y = 3x - 2 over the interval [x, x + h], you can use the formula:

Average rate of change = [f(x + h) - f(x)] / h

Substitute the function y = 3x - 2 into the formula:

Average rate of change = [(3(x + h) - 2) - (3x - 2)] / h

Simplify the expression:

Average rate of change = [(3x + 3h - 2) - (3x - 2)] / h

Average rate of change = [3x + 3h - 2 - 3x + 2] / h

Average rate of change = [3h] / h

Cancel out the common terms:

Average rate of change = 3

Therefore, the average rate of change of y = 3x - 2 over the interval [x, x + h] is 3.

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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.