Home > Calculus > Average Rate of Change Over an Interval

How do you find the average rate of change of #f(x)=-5x+2# from [2,4]?

Answer 1

#-5#

#"the average rate of change of f(x) over an interval "[a,b]# #"is the slope of the "color(blue)"secant line"" connecting the 2 points"# #(a,f(a))" and "(b,f(b))#

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

#f(b)=f(4)=-20+2=-18#

#f(a)=f(2)=-10+2=-8#

#"average rate of change "=(-18-(-8))/(4-2)#

#color(white)("average rate of change ")=-10/2=-5#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Axel Alvarez

To find the average rate of change of ( f(x) = -5x + 2 ) from ( x = 2 ) to ( x = 4 ), you use the formula:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

where ( a = 2 ) and ( b = 4 ). Substituting these values into the formula:

[ \text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} ]

[ = \frac{(-5 \times 4 + 2) - (-5 \times 2 + 2)}{2} ]

[ = \frac{(-20 + 2) - (-10 + 2)}{2} ]

[ = \frac{-18 - (-8)}{2} ]

[ = \frac{-18 + 8}{2} ]

[ = \frac{-10}{2} ]

[ = -5 ]

So, the average rate of change of ( f(x) = -5x + 2 ) from ( x = 2 ) to ( x = 4 ) is ( -5 ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.