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# Calculus Continuity Question?

I have been trying to figure this problem out:

What is c and d to make this equation continuous?

F(x)=

2x^2 + cx + d , x<-1

-2 , x=-1

dx^2 + 10x + c , x>-1

i got c=7 and d=1, and it works for the last equation, but it doesnt fit for the 1st one. Help???

### 1 Answer

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- 7 years agoFavorite Answer
for continuity, the LHS limit and RHS limit must be equal... Here, put the value of "x" as (-1) in 1st and 3rd equation as follows:

eqn 1) 2* (-1)^2 + c (-1) + d = -2 ...... (RHS is -2 because its defined in 2nd equation)

eqn 3) d (-1)^2 + 10 (-1) + c = -2

Rearranging, we get..

eqn 1) d - c = -4

eqn 3) d + c = 8

Solve them simultaneously to get c = 6 and d = 2.

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