Question

For the Function with rule f(x)=3x2^x+6, the average rate of change of f(x) between x=0 and x=2 is: help!

Answer 1

The function is not defined properly. $$ f(x)=3x2^x+6$$ ??

Answer 2

I think you just evaluate f(0), and f(2) and divide by 2

Answer 3

its supposed to be 3 (times) 2^x + 6

Answer 4

(f(2)-f(0)) / 2 should be the average rate of change

Answer 5

how did u get that?
i think you have to find the derivative first, i can do that, but im not sure what to do next

Answer 6

the derivative gives you the instantaneous rate of change at any point, but the total change divided by the x-distance is the average rate of change

Answer 7

Derivative is the instantaneous rate of change

Answer 8

but (f(2)-f(0)) / 2= f'(c) by mean value theorem.

Answer 9

with a line it's easy to see, e.g. f(x)=x, the average rate of change is 1 over any interval .. e.g. f(5)-f(2) / (5-2) = (5-2)/(5-2) = 1

Answer 10

so you just want to do f(b) - f(a) / (b-a)

Answer 11

the definition of the derivative is that quantity as b-a goes to 0

Answer 12

Indeed.

Answer 13

but if they're asking for the average over the entire interval you don't even have to differentiate, just compute f(b)-f(a) / (b-a)

Answer 14

average rate of change = (f(x2)-f(x1))/x2-x1

Answer 15

is that what your using?

Answer 16

yep

Answer 17

okay well the answer is 4.5, i dont see how 0-2 is going to give me that

Answer 18

f(0) = 9
f(2) = 18

(18 - 9) / 2 = 9/2 = 4.5

Answer 19

how did you get 9? isnt 2^0 = to 1?

Answer 20

what is f(0)? plug 0 into your original equation everywhere that x appears, what do you get?

Answer 21

ohh yepp, i see, i made a mistake. thanks!! i understand it

Answer 22

ok