Question

Find the values of c and d that make the following function f(x)=\left\lbrace \begin{array}{cl} 2 x &\mbox{if } x<1\\ cx^2+d &\mbox{if } 1\le x <2\\ 5 x &\mbox{if } x\ge 2\\ \end{array}\right.

Answer 1

A moment of reflection reveals that
2(1)=1^2 c+d
2^2 c +d = 5(2)
so
c+d=3
4 c + d =10
Solve for c and d

Answer 2

c+d =2 (Sorry)

Answer 3

\[
\left\{\left\{c\to
\frac{8}{3},d\to
-\frac{2}{3}\right\}\right\}

\]

Answer 4

^hmm interesting

Answer 5

I wonder how you come to this conclusion
2(1)=1^2c+d

Answer 6

because it was clearly stated that
f(x)=2x when x<1 and need not to be equal to 1
please correct if I'm wrong

Answer 7

The limit from both sides should be equal

Answer 8

I cannot see any evidents saying the function is continuos