Question

# Let g(x) = 21x^5 - 116x^4 + 186x^3 - 328x^2 + 369x + 60. Find g'(x)...

Let g(x) = 21x^5 - 116x^4 + 186x^3 - 328x^2 + 369x + 60. Find g'(x) and use this to find the stationary values of g(x). After finding the critical values, determine any local extrema using the FindMinimum and FindMaximum commands; state any critical values and local extrema in a text cell (x-values only).

Please explain this is Wolfram Mathematica input terms! I got most of this, but I dont know what to put for the critical values or local extrema

First we will be defining the function g(x):

• g[x_]:=21x^5 - 116x^4 + 186x^3 - 328x^2 + 369x + 60

Then we find the derivative of g(x) and put the derivative equal to zero in order to find the critical points. This can be done in two ways :

• d=D[g[x],x]
• NSolve[d==0,x]

Another way to find the critical points will be :

• NSolve[D[g[x],x]==0,x]

To find extrema of the function, here x,0,100 implies that the range of x displayed will be from x=0 to x=100. Also, we assume that the critical points lie in this range, if not then the range of x can be changed accordingly :

• FindMinimum[g[x],{x,0,100}]
• FindMaximum[g[x],{x,0,100}]

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