Find the equation of the line tangent to the given curve with the given slope. y = 2x^2-4x, with tangent line of slope 4.

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Find the equation of the line tangent to the given curve with the given slope. y = 2x^2-4x​, with tangent line of slope 4.

Eliza Beth13 · Accepted Answer

To find the equation of the line tangent to the curve y=2x2−4x with a slope of 4, we need to determine the point of tangency and then use the point-slope form of a line.First, let&#039;s find the derivative of the given curve to obtain the slope of the tangent line at any point on the curve. Taking the derivative of y=2x2−4x, we have:dydx=ddx(2x2−4x)=4x−4Setting this derivative equal to the given slope of 4, we have:4x−4=4Simplifying, we find:4x=8x=2Now, to find the corresponding y-coordinate of the point of tangency, we substitute the value of x into the original curve equation:y=2(2)2−4(2)y=8−8y=0Therefore, the point of tangency is (2,0).Now that we have the point of tangency, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is given by:y−y1=m(x−x1)where (x1,y1) is a point on the line and m is the slope of the line.Plugging in the values, we have:y−0=4(x−2)Simplifying, we find:y=4x−8Therefore, the equation of the line tangent to the curve y=2x2−4x with a slope of 4 is y=4x−8.

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