How do you find the equation of the tangent line to the curve #y=5x-2x^3# at (1,3)?

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Answer 1 · 2018-03-30T18:57:46

#y = -x + 4#

Given: #y = 5x - 2x^3#. Find tangent line at #(1, 3)#.

Find 1st derivative - the slope function:
#y' = 5 - 6x^2#

Find the slope at #x = 1#:

#"slope " = m = y'(1) = 5 - 6(1)^2 = -1#

The tangent line can be found using: #y - y_1 = m (x - x_1)#

#y - 3 = -1 (x - 1)#

#y -3 = -x +1#

#y = -x + 1 + 3#

#y = -x + 4#