SOLUTION: a line has the equation y=2x+c and a curve has the equation y= 8-2x-x^2 the line is tangent to the curve �find the value constant to c �for the case where c=11 find the x-

Question 934065: a line has the equation y=2x+c and a curve has the equation y= 8-2x-x^2
the line is tangent to the curve
�find the value constant to c
�for the case where c=11 find the x-coordinates of points of intersection of the line and the curve. Find by integration, the area of the region between the line and the curve
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The slope of the tangent line to the curve is equal to the derivative at that point.

So then set this value equal to the slope of the tangent line,

At that point, both y values are the same.

.
.
.

Two solutions,

and

Integrate between and
.
.
.

.
.
.

RELATED QUESTIONS
The line=2x+c is a tangent to the curve y=2x^2-6+20.find the value of... (answered by Alan3354,MathLover1,ikleyn)

The line y=2x+c is a tangent to the curve y=2x^2-6x+20.find the value of... (answered by math_helper)

The second derivative of a curve is y'' = 12x^2 − 8. The tangent to this curve at... (answered by Boreal,Edwin McCravy)

Find the equation of the tangent line to the curve {{{(x-y)^2}}}{{{""=""}}}{{{2x+1}}}... (answered by Edwin McCravy)

Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point... (answered by Alan3354)

Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point... (answered by Fombitz)

Find the equation of the line tangent to the following curve at the given value of x. y... (answered by solver91311)

Find the equation of the line that passes through point (0,5) and is tangent to the curve (answered by fractalier)

Find the Equation of the line that passes through point (0,5) and is tangent to the curve (answered by stanbon)