Firstly, (-1,0) is a common point thus.Originally Posted byjayson81

Substitute that into the second function,

Thus,

solve,

Thus, the second function has equation,

.

Since we say that these two function have a common tangent means the equation of the tangent through point (-1,0) is the same. Remember from analytic geomtery that two lines having same slope at same point are the same. Same thing here the tangent lines share a point thus they need to have the same slope.

The slope at for the first function is,

at is .

The slope for the second is,

at is

Thus, thus,

All we need is to find "b" in,

since (-1,0) is on the curve we have,

thus,

Thus,

Which is not true.

Thus, either you erred in the formulation of your question or there is no such numbers.