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What is the average rate of change in the interval #(-4,4)#, if #f(-4)=0# and #f(4)=-5#?

(A) #5/4#
(B) #-5/8#
(C) #5/8#
(D) #-8/5#

Answer 1

Evelyn Agard

Answer is (B)

At #x=-4#, the value of function #y=f(-4)=0#

and at #x=4#, the value of function #y=f(4)=-5#

So although from #x=-4# to #x=4#,

#x# has increased by #4-(-4)=4+4=8#,

the value of function #y=f(x)# is reduced from #0# to #-5# i.e. by #-5-0=-5#

Hence, average rate of change is #(-5)/8=-5/8# and

The response is (B).

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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 in the interval #(-4,4)#, if #f(-4)=0# and #f(4)=-5#?

(A) #5/4# (B) #-5/8# (C) #5/8# (D) #-8/5#

(A) #5/4#
(B) #-5/8#
(C) #5/8#
(D) #-8/5#