Question
For what values of a and b that make the function f continuous everywhere.
f(x)= {x−2x2−4 if x<2
ax2−bx−18 if 2< or =x<3
10x−a+b if x> or =3
f(x)= {x−2x2−4 if x<2
ax2−bx−18 if 2< or =x<3
10x−a+b if x> or =3
Answers
bobpursley
look at 2
x^2-2x-4=ax^2-bx-18
4-4-4=4a-2b-18
2a-b=-18 check that.
at x=3
ax^2-bx-18=10x-a+b
9a-3b-18=30-a+b
10a-4b=48
Now you have two equations, two unknowns, solve.
x^2-2x-4=ax^2-bx-18
4-4-4=4a-2b-18
2a-b=-18 check that.
at x=3
ax^2-bx-18=10x-a+b
9a-3b-18=30-a+b
10a-4b=48
Now you have two equations, two unknowns, solve.