SOLUTION: Determine the zeros of the f(x)=x^2-3x-4 then estimate the instantaneous rate of change in f(x) at the zeros thanks so much

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Question 1196945: Determine the zeros of the f(x)=x^2-3x-4 then estimate the instantaneous rate of change in f(x) at the zeros

thanks so much
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to determine the zeros of the f%28x%29=x%5E2-3x-4, set f%28x%29=0

0=x%5E2-3x-4...........factor
0=x%5E2%2Bx-4x-4
0=%28x%5E2%2Bx%29-%284x%2B4%29
0=x%28x%2B1%29-4%28x%2B1%29
0+=+%28x+-+4%29%28x+%2B+1%29
solutions:
if 0+=+%28x+-+4%29 =>x=4
if 0+=+%28x+%2B+1%29=>x=-1
so, zeros are -1 and 4


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-3x-4%29+


the instantaneous rate of change in f%28x%29 at the zeros:

∆y/∆x=%28f%28x2%29+-f%28x1%29+%29%2F%28x2+-+x1+%29
∆y/∆x=%28f%284%29+-f%28-1%29+%29%2F%284+-+1+%29
∆y/∆x=%28f%284%29+-f%28-1%29+%29%2F3
find f%284%29 and f%28-1%29
f%284%29=4%5E2-3%2A4-4=0
f%28-1%29=%28-1%29%5E2-3%28-1%29-4=0

then
∆y/∆x=%280+-0+%29%2F3=0%2F3=0



Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine the zeros of the f(x)=x^2-3x-4 then estimate the instantaneous rate of change in f(x) at the zeros
~~~~~~~~~~~~


Instantaneous rate of change of a function at a given point
is the value of the derivative of the function at this point.

Having this hint, complete the job on your own.


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Keep in mind that estimations given in the post by MathLover1, are absolutely   highlight%28highlight%28W-R-O-N-G%29%29.

Surely,  the meaning of the term  " estimate "  is quite wide,
but making estimation in this way as  MathLover1  does it  ( obtaining the answer  0  (zero) ),
tells that she is not familiar with the meaning of this term and does not understand what she is doing / teaching . . .


                    God,  save us from such tutors . . .