Question 1159638
<pre>
{{{f(x) = 2x^2-6x+20 }}}

f'(x) = {{{ 4x-6 }}}

For the tangent {{{ 2x+c }}} to just touch f(x), we need to find where f(x) has slope equal to 2:

    4x-6 = 2     <<< remember, the ENTIRE LHS is the slope of f(x)
     x = 2        


At x=2:  f(2) = {{{2*(2^2) - 6(2) + 20 = 8-12+20 = 16 }}}

So the tangent line {{{ 2x+c }}} just meets f(x) at x=2, hence it has value 16 there:

     2x + c = 2(2) + c = 16  ==> c = 12


Ans:  {{{ highlight(c = 12) }}}  and the tangent line is  y=2x+12, and the point of tangency is (2,16).