SOLUTION: The line=2x+c is a tangent to the curve y=2x^2-6+20.find the value of c

Algebra.Com
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
--------------------------
=2x+c is not a line
= what?
----
y=2x^2-6+20
y=2x^2 + 14
y' = 4x
======================
Answer by MathLover1(20849)   (Show Source): 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 (,)
Answer by ikleyn(52780)   (Show Source): 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.
~~~~~~~~~~~~~~~~


            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

Solved.


RELATED QUESTIONS

The line y=2x+c is a tangent to the curve y=2x^2-6x+20.find the value of... (answered by math_helper)
a line has the equation y=2x+c and a curve has the equation y= 8-2x-x^2 the line is... (answered by Fombitz)
A curve is given: y = e^-x^2. Find the point on the curve where the slope of the tangent... (answered by Fombitz)
Find two points on the curve (C)······ x^2 y+y^4 +6=4+2x, where x = 1. At each of those (answered by Fombitz)
The tangent to the curve y = 2x^2 + ax + b at the point (-2,11) is perpendicular to the... (answered by math_tutor2020)
Consider the curve described by the equation below, y = e^2x + 3. a) Sketch a rough... (answered by solver91311)
find the value of k for which the line y=x+k is a tangent to the curve y to the power of... (answered by Edwin McCravy)
Stuck on question 3 which is about equation of the tangent! Curve c has equation... (answered by Cromlix)
The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the... (answered by richwmiller,jim_thompson5910)