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Find the value of k if the line y = x + k is tangent to the graph of y = x^2.

 Jul 2, 2020
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The slope of  y  =  x + k  is 1.

 

We need to find where the slope of  y  =  x2  is 1.

Find the first derivative of y:  y'  =  2x     This formula will give us the slope of  y  =  x2  at every point.

When does  2x  =  1?     --->     x  =  1/2.

So, when  x  =  1/2,  the slope of   y  =  x2  is 1.

When  x  =  1/2,  y  =  x2   --->   y  =  (1/2)2  =  1/4.

So the point of intersection of the line and the parabola is the point  (1/2, 1/4).

 

The equation of the line will be:  y - 1/4  =  1(x - 1/2)   --->   y  =  x - 1/4

 Jul 2, 2020

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