f(x) = 4x2 + 3x + 5 . using the Mean Value Theorem on the interval [-1,1]. That is, find a number c at which the instantaneous rate of change of the function f equals the average rate of change of f over the interval [-1,1].

Question

anonymous · Answer

i used the mean value theorm  f'(c)=f(1)-f(-1)/1-(-1)

myininaya · Answer

and you can find f(1) and f(-1)
from f(x)=4x^2+3x+5

anonymous · Answer

which equate to 8x+3=3

anonymous · Answer

does that mean no c value exists?

myininaya · Answer

nope that means you need to solve 8c+3=3
for c

anonymous · Answer

c=0/8

myininaya · Answer

if c occurs in the interval [-1,1]
then there does exist a c in the interval [-1,1]
such that f'(c)=(f(b)-f(a))/(b-a)

myininaya · Answer

c=0 is a number between -1 and 1

myininaya · Answer

you are done!

anonymous · Answer

oh right! thanks

myininaya · Answer

You do understand that 0/8=0 (and not undefined)
if we had 8/0 (we wouldn't have found a number)

anonymous · Answer

yea...........i got confused about that i was thinking that it was undefined opps

myininaya · Answer

Yeah a lot of people do get confused about that

always tried to tell them over and over 
if 0 is on top, you have 0
however if you have 0 on bottom, it is undefined

myininaya · Answer

but if you have study limits you also know 0/0 is indeterminate form

anonymous · Answer

thanks