Question

For what values of a and b is the line 3 x + y = b tangent to the curve y = a x^{3} when x = -2?

Answer 1

Hello,

The tangent point T is (-2,a(-2)^3) or (-2,b-3*(-2))
The slope of the curve in T is -3 (slope of the line)

y=ax^3==>y'=3ax²==>y'(-2)=3*a*4=-3 ==>4a=-1 ==>a=-1/4

T=(-2,-1/4*(-2)^3))=(-2,2)

b-3*(-2)=2==>b=2-6==>b=-4