hi all pls all
Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12
please solve the entire equation with explanation please. ty.
Since the line is written in slop intercept form
we know that the slope of line is
Since we need the slope to equal the derivative we get...
solving for x we get
This gives us half of the ordered pair...
plugging this into the equation of the parabola we get
This completes our ordered pair giving us (1,-12)
Now finally we use this ordered pair to solve for c plugging the ordered pair into the equation of the line we get....
solving for C we finally end up with...
I hope this helps. Remember that the derivative represents the slope of the graph at any point.