Given the function , indicate the maximum or minimum point for the graph of the function.

Answer 1

for a function f(x)

find the relative minimum or maximum by taking the derivative and setting it equal to zero

f'(x) = 0

then solve for x. then plug that x value back into f(x) to get the maximum or minimum y value.

for example f(x) =x^2

f'(x) = 2x = 0, x= 0

the minimum point is f(0) = (0)^2 = 0

or for example f(x) = x^3 + (3/2)x^2 - 90x + 5

f'(x) = 3x^2 + 3x - 90 = 0

x^2 + x -30 = 0

(x-5)(x+6) = 0

x=-6 or 5 = the x coordinate of the relative maximum or minimum point

to find the y value, plug that x coordinate into f(x), the cubic polynomial.

Answer 2

What is the function?