What is the slope of f(t) = (t-1,t+3)f(t)=(t1,t+3) at t =1t=1?

1 Answer
Feb 16, 2016

11

Explanation:

The derivative of the parametric function

f(t)=(x(t),y(t))f(t)=(x(t),y(t))

is

f'(t)=(x'(t))/(y'(t))

The given parametric function is

f(t)=(t-1,t+3)

which means that

x(t)=t-1
y(t)=t+3

Differentiation of both functions with respect to t yields

x'(t)=1
y'(t)=1

so the entire parametric function's derivative is

f'(t)=(x'(t))/(y'(t))=1/1=1

This means that, irrespective of the value of t, the slope of the tangent line to the function is always 1.