clara1223
  • clara1223
Determine the values of the constants B and C so that the function given below is differentiable. f(x)={8x^3 when x≤1; (Bx^2)+Cx when x>1} a) {B=−24,C=24} b) {B=24,C=32} c) {B=16,C=−8} d) {B=24,C=40} e) {B=−48,C=−8}
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
plug in \(x=1\) set them equal take the derivative, plug in \(x=1\) and set those equal solve for B, C
anonymous
  • anonymous
for example the first equation you get is \[8=B+C\]
clara1223
  • clara1223
once i have 8=B+C and 24=2B+C how do I solve for B and C?

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clara1223
  • clara1223
anonymous
  • anonymous
same way you solve any system of equations \[B+C=8\\ 2B+C=24\] elimination or substitution
anonymous
  • anonymous
or just subtract equation one from equation two and get \[B=16\] right away
clara1223
  • clara1223
figured it out! thanks!

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