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)

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)

amistre64 · Answer

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

anonymous · Answer

How do I find the slop in this case?

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

Oh, the slope is -3 right?

amistre64 · Answer

yes

amistre64 · Answer

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?

amistre64 · Answer

|dw:1383597837128:dw|

amistre64 · Answer

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

amistre64 · Answer

|dw:1383597983898:dw|