Question

For what value of the constant ( c ) is the function ( f ) continuous on ( (-infty, infty) ) ? [ f(x)=left{egin{array}{ll} c x^{2}+2 x & ext { if } x<2 \ x^{3}-c x & ext { if } x geqslant 2 end{array} ight. ] Answer + [ frac{2}{3} ] (for what ( mathrm{c} ) is ( mathrm{f} ) continuous everywhere?) Also sketch a graph of ( f(x) ) for the value of ( c ) that you found.

          For what value of the constant ( c ) is the function ( f ) continuous on ( (-infty, infty) ) ?
[
f(x)=left{egin{array}{ll}
c x^{2}+2 x & 	ext { if } x<2 \
x^{3}-c x & 	ext { if } x geqslant 2
end{array}
ight.
]
Answer +
[
frac{2}{3}
]
(for what ( mathrm{c} ) is ( mathrm{f} ) continuous everywhere?) Also sketch a graph of ( f(x) ) for the value of ( c ) that you found.

$For what value of the constant ( c ) is the function ( f ) continuous on ( (-infty, infty) ) ? [ f(x)=lefteginarrayll c x^2+2 x ext if x<2 x^3-c x ext if x geqslant 2 endarray ight. ] Answer + [ frac23 ] (for what ( mathrmc ) is ( mathrmf ) continuous everywhere?) Also sketch a graph of ( f(x) ) for the value of ( c ) that you found.$

Added by Steve A.

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