Find the value of k

Question

A curve has a gradient function of 2x-k, where k is a constant. If the tangent to the curve at the point (3,6) passes through origin, find the value of k

Answer 1

If the tangent at (3,6) passes through the origin, then its slope m = 6/3 = 2.

 

But this m must also equal 2(3) - k, according to the stated gradient function 2x - k.

 

Therefore m = 2 = 6 - k from which k = 4.