The slope of the tangent to the curve y = 3x2 + 2kx - 5 at x = 1 is 9…

$y = 3x^2+2kx-5⇒\frac{dy}{dx}=6x+2k$

∴ Slope of tangent at x = 1 is 9

$6(1)+2k=9$

$6+2k=9⇒2k=9-6⇒2k=3$

$k=\frac{3}{2}$