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How do you find the average rate of change of #f(x)=-3x^2+2# between [0,3]?

Answer 1

Eva Adamson

Average rate of change#=-9#

The average rate of change is denoted by this formula

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

Let #a=3# and #b=0#,

#(f(3)-f(0))/(3-0)#

Expand,

#((-3(3)^2+2)-(-3(0)^2+2))/3#

Simplify,

#(-25-2)/3#

Solve,

#-9#

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Answer 2

Avery Alexander

To find the average rate of change of ( f(x) = -3x^2 + 2 ) between ( x = 0 ) and ( x = 3 ), you use the formula: [ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ] Substitute the values ( a = 0 ) and ( b = 3 ) into the formula: [ \text{Average Rate of Change} = \frac{f(3) - f(0)}{3 - 0} ] [ \text{Average Rate of Change} = \frac{-3(3)^2 + 2 - (-3(0)^2 + 2)}{3} ] [ \text{Average Rate of Change} = \frac{-27 + 2 - 2}{3} ] [ \text{Average Rate of Change} = \frac{-27}{3} ] [ \text{Average Rate of Change} = -9 ]

Therefore, the average rate of change of ( f(x) = -3x^2 + 2 ) between ( x = 0 ) and ( x = 3 ) is ( -9 ).

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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.