A and B
Calculus
Level
2
Look for a and b so that the line y = -3x + 4 is tangent to the graph of y = ax^3 + bx at x = 1. What is the sum of a and b?
-2
3
4
1
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1 solution
If the line is tangent to the cubic at x = 1 , then both must intersect at that point.
The y-value on the line at x = 1 is: ( − 3 ) ( 1 ) + 4 = 1
The y-value on the curve at x = 1 is: 1 3 ( a ) + ( 1 ) b = a + b
Since both y-values must be the same since the line is tangent to the curve, a + b = 1