anonymous
  • anonymous
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.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Owlcoffee
  • Owlcoffee
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
  • anonymous
Take the first derivative of f(x), f'(x)=y'=slope. Let y'=0 to evaluate the value to the slope.
dumbcow
  • dumbcow
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: \[y = f'(x_1) (x - x_1) + y_1\] \[(x_1,y_1) = (-1, f(-1))\] \[(x_1,y_1) = (1/3, f(1/3))\]

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