Question

Find the minimum or maximum value of the function g(x) = -x2 + 3x - 2. Then state the domain and range of the function.

Answer 1

Think about the sign of the derivative
\[
g'(x) -3 x +3
\]

Answer 2

\[g(x) = -x^2 + 3x - 2\]

Answer 3

g'[x] =0 when x =1, since g'(x) > 0 for x <1 and g'(x) <0 for x>1
at x =1, g has a maximium

Answer 4

Domain all real numbers

Answer 5

range x<= g[1]=0

Answer 6

find the first derivative and solve for when the function equals zero. That will give you the x for the point of the maximum/minimum
if you want to know the y coordinate then you plug in the x to the original and get your y.


Then to see whether the point is a maximum or minimum you find the second derivative and see whether the value is negative or positive.

If it's positive the values is minimum
if it's negative the value is maximum

Answer 7

THANKS FOR YOUR HELP!