Question

What is the local maximum value of the function? g(x)=x³+5x²-17x-21 (Round answer to the nearest thousandth.)

Answer 1

Answer:

g(x)=65.671

Step-by-step explanation:

It's local maximum value will be at a place where the function g(x) just turns from positive slope to a negative slope, ie. g'(x)=0

$g(x)=x^{3} + 5x^{2} -17x-21\\g'(x)=3x^{2} +10x-17$

The equation starts from the -∞ and rises till its slope gets zero for the first time, so the least value of x that satisfies g'(x) will provide the required result.

Roots of x=$\frac{-10\frac{+}{}\sqrt{304} }{6}$

Least value will be the one with the negative sign ie.$\frac{-10-\sqrt{304} }{6}$

Plugging it into the equation we get, g(x)=65.671

Answer 2

Answer:

g(x)=65.671

Step-by-step explanation: