Question

For what values of a and b is the line −4x+y=b tangent to the curve y=ax^3 when x=3?

Answer 1

find the slope of each at 3 and the b value that makes them have the same y values at 3

Answer 2

y = 4x + b has a slope of 4
and
y = ax^3 has a slope of ...

Answer 3

3a ?

Answer 4

close, 3ax^2, and when x = 3, that equals...

Answer 5

so the slope is 3ax^2 even thou y=mx+b m being the slope?

Answer 6

Evaluate 3ax^2, where x = 3 to get 3a(3)^2 = 27a
27a is the slope at x = 3, and it has to equal 4 to be tangent to the line, so solve
27a = 4 to find a, then work on b the same way you would for an intersection of two functions.