How do you find the local maximum and minimum values of g(x)=x^3+5x^2-17x-21?

1 Answer

Local Maximum : (-4.57259929569, 65.6705658828)
Local Minimum : (1.2392659623, -32.48538069)

Explanation:

From the given equation
y=x^3+5x^2-17x-21

take the first derivative

y'=d/dx(x^3)+d/dx(5x^2)+d/dx(-17x)+d/dx(-21)

y'=3x^2+10x-17

Set y'=0 then solve for x

3x^2+10x-17=0

x=(-10+-sqrt((10)^2-4(6)(-17)))/(6)

x=(-10+-sqrt(304))/(6)

to values for x:

x_1=-4.57259929569
and

x_2=1.2392659623

Solve for corresponding values of y using y=x^3+5x^2-17x-21 and the points are

Local Maximum: (-4.57259929569, 65.6705658828)
Local Minimum : (1.2392659623, -32.48538069)

Kindly see the graph below for better view

Desmos.comDesmos.com

God bless....I hope the explanation is useful.