What is the function derivative?

If you know that a function f(x) is positive everywhere, what can you conclude from that about the derivative f’(x)?: a) the derivative is positive everywhere b) the derivative is increasing everywhere c) the derivative is concave upward, d) you can...

f(x) = x^4 has a derivative everywhere, has a critical point at x = 0 but has no relative extrema.Give an explicit formula for a function g(x) that has a derivative everywhere, has exactly two critical points

the function is (x^2)/(1 + (x^5)). essentially x squared over quantity 1 plus x to the fifth power. could you show me how to do take the anti-derivative of this function?

What is the derivative of ye^(x^2) with respect to x. What is the derivative of xe^y with respect to x and y

What is the difference between both derivatives? What happens if a body in a specific position has dv/dt = 0 , but {\partial v}/{\partial t} !=0 ?

Consider the function f(x) whose second derivative is f '' (x)= 4x+2sin(x) . If f(0)=2 and f ' (0)=2 , what is f(x)?

What is the derivative of the function. f(x) = ln (x+9/x-9)