Applications of Derivatives

[patelkey]

Problem Statement: It is true that Q(x) = x^5 + x^3 +x is a one to one function whose domain and range are all numbers.

a.) Suppose that R is the function inverse to Q. here is no simple algebraic way to compute values of R. Compute R(3), first derivative of R(3), and second derivative of R(3).

Information that I know:
Q(R(x))=x and R(Q(x))=x. I have to find an input to Q which will output 3. hen differentiation one of the equations, maybe more than once.
I know that R(1)=3 and R(3)=1

[lurflurf]

hint: determine if Q(t) is monotone.
first derivative of R(3), and second derivative of R(3) are 0 since R(3) is not a function of t pehaps R'(3) and R''(3) are desired? The derivative and second derivative of a function can be easily found from the derivatives of the inverse, hint differentiate Q(R(x))=x.

[patelkey]

So then I would get
R(3)=1
first derivative of R(3)=1
and second derivative of R(3)=0