Determine the value of K that will cause f(x)=Kx^2+4x-3 to intersect the line g(x)=2x-7 at one point. SHOW ALL YOUR STEPS, DON'T USE DECIMALS INSTEAD USE FRACTIONS PLEASE

Given:

The function are:

The graph of f(x) intersect the line g(x) at one point.

To find:

The value of K.

Solution:

The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.

We have,

Differentiate this function with respect to x.

Let the point of tangency is . So, the slope of the tangent line is:

On comparing with slope-intercept form, we get

So, the slope of the tangent line is 2.

Putting in g(x), we get

Putting in the above equation, we get

Putting and in f(x).

Multiply both sides by K.

Therefore, the value of K is .

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step-by-step explanation: