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If f(x)=(2x^5)/2, find f'(4). Find the equation of the tangent line to the curve y =...

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jmg5639 | Student, Undergraduate | Honors

Posted January 29, 2013 at 5:00 PM via web

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If f(x)=(2x^5)/2, find f'(4). Find the equation of the tangent line to the curve y = (2x^5)/2 at the point (4, f(4)).

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 29, 2013 at 5:10 PM (Answer #1)

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The function f(x) = (2*x^5)/2 = x^5

f'(x) = 5*x^4

f'(4) = 5*256 = 1280

The equation of the line tangent to the curve at (4, f(4)) is:

(y - 1280)/(x - 4) = 1280

=> y - 1280 = 1280x - 5120

=> y = 1280x - 3840

The equation of the tangent is y = 1280x - 3840

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