Hybrid Graph

By Rocky On February 17, 2010 Under Mens Golf Clubs

Hybrid Graph
Hybrid Discontinuity Question?

For two graphs to join smoothly, the gradients on both sides have to be equal.

g(x) = { x + 1, x<2}
{ ax^2 + bx, x>=2 }

Find the values of a and b so that both graphs join smoothly.

for them to be continuous, the limit from both ends must be the same.
so find the limit as x tends to 2 from left and right, whatever that value is, that is what will help you find one of the 2 variables.

the next thing is, the derivative at 2 must be the same from both the left and the right,
Find the derivative at 2 and apply that to the second equation derivative.
that will give you the latter of the 2 variables.

hope this helps.

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