Find k such that the line [y=5x-4] is tangent to the function : x^2-kx
To find the value of k such that the line y = 5x - 4 is tangent to the function x^2 - kx, we need to set the derivative of the function x^2 - kx equal to the slope of the line, which is 5.
Step 1: Find the derivative of the function x^2 - kx:
Take the derivative of x^2 with respect to x, which is 2x.
Take the derivative of -kx with respect to x, which is -k.
Therefore, the derivative of x^2 - kx is 2x - k.
Step 2: Set the derivative equal to the slope of the line:
2x - k = 5
Step 3: Solve for x:
2x = 5 + k
Divide both sides by 2: x = (5 + k) / 2
Step 4: Substitute the value of x back into the original function to find k:
Substituting x into the function x^2 - kx, we get:
(5 + k) / 2)^2 - k((5 + k) / 2) = 0
Simplifying this equation will give you a quadratic equation in terms of k. Solve the quadratic equation for k to find the value that satisfies the condition for the line to be tangent to the function.