Answer:
Hence, the slope ,
Step-by-step explanation:
We need to find the slope, i.e. .
and all the functions are in terms of .
So this looks like a job for the 'chain rule', we can write:
Given the functions
and
we can differentiate them both w.r.t to
first we'll derivate Eq(B) to find dx/dt
we can also rearrange Eq(B) to find x in terms of t , . This is done so that is only in terms of t.
we can find the value of this derivative using t = 3, and plug that value in Eq(A).
now let's differentiate Eq(C) to find dy/dt
rearrange Eq(C), to find y in terms of t, that is . This is done so that we can replace y in to make only in terms of t
we can find the value of this derivative using t = 3, and plug that value in Eq(A).
Finally we can plug all of our values in Eq(A)
but remember when plugging in the values that is being multiplied with and NOT , so we have to use the reciprocal!
our slope is equal to