Question
Let c(t) = (712 – 5,5t2 – 30t). Find the equation of the tangent line at...
Let c(t) = (712 – 5,5t2 – 30t). Find the equation of the tangent line at t = 3. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y(x) =
Answers
Sala Clt) = (7-5, 5#-306) at t=3 To find the equation of the tangent line, we need Slope m= dy and the point of tangency (0o, yo) Then the equation is the usual y - yo = m 18-760) O we have the parametric curve x=72²-5 , y = 5t² - 30t so we compute, at = 14+ ; dy = 106-30 Then dy dyldt 10t - 30 14 t doc doc/dut 1013)-30 - 0 I at t =3 a And slope at gives. (m) = o . t = 3 then the original equation ( 58 , -45) (20,.) Now we put in line: the equation ☺ for the tangent y-Yo = m (x-Xo) = 0 (x–58) y +45 = 0 y- (-45) = (9(*) = - 451 -45
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