Determine the values of the constants B and C so that the given function is differentiable. f(x)=5x^3 when x1

Question

Determine the values of the constants B and C so that the given function is differentiable.

f(x)=5x^3 when x<or=1
f(x)=Bx+C when x>1

anonymous · Answer

I've found the limit approaching from the left to be 5 and the limit approaching from the right to be B+C. B+C=5

anonymous · Answer

That is a piecewise function by the way.

zepdrix · Answer

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if i remember correctly.. for it to be continuous .. the slopes need to be equal from the left and right as well. so f'(x) needs to be equal in the limits.
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