Question

Does there exist a continuous function f(x) such that f(0)=−3, f(2)=−9 and f′(x)≤−7 for all x in (0,2)

Answer 1

what is the slope between f(0) and f(2) ?

Answer 2

How do I find the slop in this case?

Answer 3

you are given 2 points ... (0,-3) and (2,-9)

Answer 4

the formula for the slope between 2 points was worked out back in algebra classes ....

Answer 5

Oh, the slope is -3 right?

Answer 6

yes

Answer 7

now, the best we can do to get from one point to the other; we are told is, -7 can you tell me if this is possible?

Answer 8

IF the slope between the points had been "less than or equal to" -7, we could have found a way to accomplish it; but as is, we cant even hit the second point