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What is the average rate of change of the function #f(x) = 2x^2 - 3x - 4# for #-3<=x<=-1#?

Answer 1

William Abdalla

-11

the average rate of change can be found using

# (f(b) - f(a))/(b-a) #

in this question :# (f(-1) - f(-3))/(-1 -(-3)) #

now f(-1) =#2(-1)^2 - 3(-1) - 4 = 1 #

and f(-3) # = 2(-3)^2 - 3(-2) - 4 = 23#

#rArr (1 - 23)/(-1-(-3)) = -22/2 = -11#

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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.

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What is the average rate of change of the function #f(x) = 2x^2 - 3x - 4# for #-3&lt;=x&lt;=-1#?

What is the average rate of change of the function #f(x) = 2x^2 - 3x - 4# for #-3<=x<=-1#?