Final answer:
To find the value of k so that the function f(x) = x^2 + kx is tangent to the line y = 2x - 9, equate the slopes of the function and the line to find the value of x. Plug this value of x back into the function to find the value of k.
Step-by-step explanation:
To find the value of k so that the function f(x) = x^2 + kx is tangent to the line y = 2x - 9, we need to find the value of k that makes the slopes of the function and the line equal.
The slope of the given line is 2. The slope of the function can be found by taking the derivative of f(x):
f'(x) = 2x + k
Setting the slope of the function equal to the slope of the line:
2 = 2x + k
Solving for x:
x = -k/2
Substituting this value of x back into the function equation:
f(-k/2) = (-k/2)^2 + k(-k/2)
To make the function tangent to the line, the value of -k/2 should be the x-coordinate of the point of tangency.
So, the value of k that makes the function tangent to the line is -2.