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.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

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.
Take the first derivative of f(x), f'(x)=y'=slope. Let y'=0 to evaluate the value to the slope.
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: \[y = f'(x_1) (x - x_1) + y_1\] \[(x_1,y_1) = (-1, f(-1))\] \[(x_1,y_1) = (1/3, f(1/3))\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question