Critical pints of f in Let f(x)=x3+27x+4

Critical points: none

Step-by-step explanation:

We are given the function;

f(x)=x³+27x+4

We are required to determine the critical points

First we can find the derivative of the function;

Thus, the derivative will be;

But, at critical point the derivative is equal to zero or undefined

Therefore;

Thus, the function has no critical points

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)