Question 637344
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
What is the value of the slope of the tangent to the curve at x = +2
f (x) = x ^ 3 - x ^ 2 - 2x      | Taking the 1st Derivative    
f '(x) = {{{3x^2 - 2x  - 2}}} 
f '(2) = {{{3*4 - 2*2  - 2 = 6}}} , the slope-value 
y = mx + b
 {{{y = highlight(6)x + b}}}    |Using (x,y) coordinate (2,0) to solve for b, {{{f(2) = 8-4-4 = 0}}}
 0 = 12 + b
-12 = b
EQ of the tangent line at x = 2 is y = 6x-12
{{{drawing(300,300,   -6, 6, -6, 6,  grid(1),
circle(2, 0,0.3),
graph( 300, 300, -6, 6, -6, 6,0,6x-12,x^3 - x^2 - 2x  ))}}}