Question 1159785: The line=2x+c is a tangent to the curve y=2x^2-6+20.find the value of c Found 3 solutions by Alan3354, MathLover1, ikleyn:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The line=2x+c is a tangent to the curve y=2x^2-6+20.find the value of c
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=2x+c is not a line
= what?
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y=2x^2-6+20
y=2x^2 + 14
y' = 4x
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You can put this solution on YOUR website!
The line is a tangent to the curve (assuming you have )
find the value of c
first derivate:
'
For the tangent to just touch , we need to find where has slope equal to :
-> remember, the entire LHS is the slope of
At :
So the tangent line just meets at , hence it has value there:
then
your answer is:
and the tangent line is , and the point of tangency is (,)
You can put this solution on YOUR website! .
The line y = 2x+c is a tangent to the curve y = 2x^2-6x+20. Find the value of c.
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Notice that I EDITED your post, since it was nonsensical in your original version.
Actually, it is of the pure Algebra problem, and can be solved using Algebra methods,
without disturbing Calculus.
You simply need to find the unique common points of the straight line and the parabola.
Watch my steps.
I will search for a unique common point of the straight line and the parabola.
So, I write this equation
2x + c = 2x^2 - 6x + 20 (1)
and simplify it
2x^2 - 8x + (20-c) = 0. (2)
Next I calculate the discriminant
d = = (-8)^2 - 4*2*(20-c) = 64 - 160 + 8c = 8c - 96.
Since I want to have a unique root of the quadratic equation (1) ( or (2) ), I equate the discriminant to 0 (zero)
8c - 96 = 0,
and I get the solution immediately
c = 96/8 = 12. ANSWER
