Question

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

Answer 1

Answer:

-3/2

The problem:

Find $c$ so the function $f$ is continuous.

$f(x)=cx^2+6x, x$

$f(x)=x^3-x,x \ge 2$

Please read my interpretation of the problem above.

Step-by-step explanation:

If we want $f$ continuous at $x=a$, then we want the following things:

$\lim_{x \rightarrow a}f(x)=f(a)$ (This means the left and right limits at $x=a$ need to equal.)

Of course the limit and $f(a)$ need to both be a number.

So we want to basically solve the following equation:

$c(2)^2+6(2)=(2)^3-(2)$

$c(4)+12=8-2$

$4c+12=6$

Subtract 12 on both sides:

$4c=-6$

Divide both sides by 4:

$c=\frac{-6}{4}$

Reduce:

$c=\frac{-3}{2}$