For what value of the constant c is the function f continuous on the interval (−[infinity],[infinity]). f(x)={cx2+6x, x 3−x, x< 2 x≥2

-3/2

The problem:

Find so the function is continuous.

Please read my interpretation of the problem above.

Step-by-step explanation:

If we want continuous at , then we want the following things:

(This means the left and right limits at need to equal.)

Of course the limit and need to both be a number.

So we want to basically solve the following equation:

Subtract 12 on both sides:

Divide both sides by 4:

Reduce:

3/6   and 9/18

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4