Make a sign diagram for the derivative of the function. f(x)=x+4x38x² +62 f'(x) [ increase 0 decrease f'(x) 0 Sketch the graph of the function. f'(x) f'(x) Find all open intervals of increase and decrease. (Enter your answers using interval notation.) 0 f'(x) 0 f'(x) 0

Introduction:

Any interval in the domain of a function's derivative can be utilized to assess whether the function is increasing or decreasing. The function is said to be rising on I if $f\prime \left(x\right) > 0$ at each point in the interval I. It is claimed that a function is declining on an interval I if $f\prime \left(x\right)<0$ at every point in the interval. The derivative must be positive or negative at all other locations where the function exists since it is zero or does not exist only at the crucial points of the function.