anonymous
  • anonymous
What is the average rate of change of the function f(x)= X^2-4x+7 on the interval 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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dumbcow
  • dumbcow
basically its the slope formula: f(3) -f(1)/ 3-1
anonymous
  • anonymous
how did u get that?
campbell_st
  • campbell_st
find f(1) and f(3) average rate of change is \[m = [(f(3) - f(1)]/(3 - 1)\]

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dumbcow
  • dumbcow
rate of change = slope technically avg rate of change is defined as: \[\frac{1}{b-a}\int\limits_{a}^{b} f'(x) dx = \frac{f(b) -f(a)}{b-a}\]
anonymous
  • anonymous
so can i use m= Y2-Y1/X1-X2 ?
dumbcow
  • dumbcow
yep the avg slope in that interval is the same as the slope of the line connecting the 2 endpoints
anonymous
  • anonymous
0/2 ?
dumbcow
  • dumbcow
ok yeah thats it. 0/2 = 0 so the avg slope is 0
anonymous
  • anonymous
g(x)=mx+b, x1
anonymous
  • anonymous
Without doing any calculation, how can one determine the average rote of change of g(x)= mx+b over the interval X1
dumbcow
  • dumbcow
just plug it into the formula g(x2)-g(x1)/ x2-x1
anonymous
  • anonymous
and then ?
anonymous
  • anonymous
finish?
dumbcow
  • dumbcow
simplify, you should find that things cancel
anonymous
  • anonymous
mX2-mX1/X2-X1 ?
dumbcow
  • dumbcow
yep, now factor out the m
anonymous
  • anonymous
answer is m ?
dumbcow
  • dumbcow
yep :)
anonymous
  • anonymous
If f(x)=1/3^x and g(x)=x^3, what is the domain of (f.g)(x)?
anonymous
  • anonymous
(f into g)(x)
anonymous
  • anonymous
{x E R} ?
dumbcow
  • dumbcow
so you are plugging g(x) into the variable for f --> 1/3^g(x) = 1/3^(x^3) domain is all possible x_values
anonymous
  • anonymous
(f.g)(x) divided
anonymous
  • anonymous
f(x).g(x)
anonymous
  • anonymous
multiply
dumbcow
  • dumbcow
??
anonymous
  • anonymous
f(x) and g(x) are multiply
dumbcow
  • dumbcow
1/3^x * x^3
anonymous
  • anonymous
yeah
dumbcow
  • dumbcow
thats it
anonymous
  • anonymous
what is the domain?
dumbcow
  • dumbcow
oh, all real num there is no x value that makes it undefined
anonymous
  • anonymous
{x E R} ? x is not equal -1 ?
dumbcow
  • dumbcow
umm well R is used as notation for the set of all real numbers
anonymous
  • anonymous
i mean x can't be equal -1 or x can't be equal 0 or x can't be equal 1 or just { x E R } ?

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