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Question
Hay, I hope you can help me.
Let F(x) be the function defined below:
[x^2 -4xk+3h , x>or=4
F(x)[k , -2<x<4
[(3/2)x^3 *k-3xh , x<or=-2
Find the values of k and h so that F(x) is continuous everywhere. Justify your answers. k and h are constants.
I would very much appreciate your help with this one.
Thanks,
Jon
Is this suppose to be
F(x) = 1.5kx^3 - 3xh for x≤-2,
F(x) = k for -2≤x≤4, and
F(x) = x^2 -4xk+3h for 4≤x?
At x=-2, it is known that F(-2) = -12k + 6h and F(-2) = k.
This will lead to 6h = 11k.
This says the [1] h=11k/6.
At x=4, it is known that F(4) = k and F(4)=16-16k + 3h.
Since we know that F(4) must be the same, take the equation
k = 16 - 16k + 3h and put in h = 11k/6.
Solve the equation for k.
Use equation [1] to find h.
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