A curve in a plane is defined parametrically by the equations x = t^3 + t and y = t^4 + 2t^2. What is the equation of the line tangent to the curve at t = 1?

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Answer 1 · 2018-05-12T13:48:28

The equation is #y=2x-1#

The curve is defined parametrically by

#{(x=t^3+t),(y=t^4+2t^2):}#

The slope is

#(dy)/dx=(dy/dt)/(dx/dt)#

#dy/dt=4t^3+4t#

#dx/dt=3t^2+1#

Therefore, when #t=1#

#dy/dx=(8)/(4)=2#

The equation of line tangent to the curve is

#y-3=2(x-2)#

#y-3=2x-4#

#y=2x-1#