Homework Help

Find the slope of the tangent line to y=x^5-3x^-3 at x=-2

user profile pic

tkniz | Student, Undergraduate | eNoter

Posted May 3, 2011 at 11:00 PM via web

dislike 1 like

Find the slope of the tangent line to y=x^5-3x^-3 at x=-2

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 3, 2011 at 11:33 PM (Answer #1)

dislike 1 like

The slope of a tangent line to a curve at any point is the value of the first derivative at that point.

The function we have is y = x^5 - 3x^(-3)

y' = 5x^4 - (-3*3)x^(-4)

=> y' = 5x^4 + 9x^-4

At x = -2

y' = 5*(-2)^4 + 9*(-2)^(-4)

=> 5*16 + 9/ 16

=> 1289/16

The slope of the tangent to the curve y=x^5-3x^-3 at x=-2 is 1289/16

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes