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 x1}
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}

Question

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}

anonymous · Answer

plug in $x=1$ set them equal 
take the derivative, plug in $x=1$ and set those equal 
solve for B, C

anonymous · Answer

for example the first equation you get is $$8=B+C$$

clara1223 · Answer

once i have 8=B+C and 24=2B+C how do I solve for B and C?

clara1223 · Answer

@satellite73

anonymous · Answer

same way you solve any system of equations 
$$B+C=8\
2B+C=24$$ elimination or substitution

anonymous · Answer

or just subtract equation one from equation two and get $$B=16$$ right away

clara1223 · Answer

figured it out! thanks!