Find the equation of each tangent of the function f(x) = x^3+x^2+x+1 which is perpendicular
to the line 2y + x + 5 = 0.

Question

Find the equation of each tangent of the function f(x) = x^3+x^2+x+1 which is perpendicular
to the line 2y + x + 5 = 0.

owlcoffee · Answer

First, you should derivate the function to obtain the slope of each tangent line to it, deduce the slope of the given line and then just find the perpendicular slope.
You will obtain a parametric equation and you'll have to solve for the parameters.

anonymous · Answer

Take the first derivative of f(x), f'(x)=y'=slope.
Let y'=0 to evaluate the value to the slope.

dumbcow · Answer

the slope of given line is -1/2
--> y = -(x+5)/2

the perpendicular slope of -1/2 is 2
set derivative equal to 2 to find all points where slope of tangent line is 2

---> 3x^2 +2x+1 = 2

solutions --> x = -1, 1/3

equation of tangent line:
$$y = f'(x_1) (x - x_1) + y_1$$
$$(x_1,y_1) = (-1, f(-1))$$
$$(x_1,y_1) = (1/3, f(1/3))$$