Question

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

Answer 1

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

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