part of the curve y=k(x-2)^3,k is constant.The curve intersects the straight line x=4 at point A.At point A dy/dx =36 .Find the value of k.

Question

there is a diragram but I can't show it here

Answer 1

y = k(x - 2)³

 

dy/dx = 3k(x - 2)²

 

At x = 4, dy/dx = 36.

 

36 = 3k(4 - 2)² = 3k(2²) = 12k

 

36 = 12k

 

k = 3