Question

How do you find k such that the line is tangent to the graph of the function function: `f(x) = x^2 - kx` and line: y=4x - 9?

Answer 1

A step to get you started.

Explanation:

A tangent can only occur when the two lines have a common point.

Not only that, it must mean that at that point they have the same gradient. So:

`f'(x)" " ->" " m " in " y=mx+c" " ->" "y=4x-9`

Thus `f'(x)=2x-k =4`.................................Equation(1)

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Consider that at the tangential point they both have the same coordinates.

`=>f'(x)=x^2-kx = y = 4x-9`

`x^2-kx=4x-9`

`x^2-x(k+4)=9`......................................Equation(2)

Now solve as simultaneous equations.

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`2x-k =4`.................................Equation(1)
`x^2-x(k+4)=9`......................................Equation(2)