# 12th Calculus

posted by .

use the derivative of the function
y=f(x)to find the points at which f has a

local maximum
local minimum
point of inflection

y'=(x-1)^2(x-2)(x-4)

• 12th Calculus -

if f(x)=uvw
then
f'(x)=uvw'+ uwv'+ wvu'

• 12th Calculus -

I will assume you really meant to write the derivative y' and not the function y although I would have thought the book would ask you to find that derivative.

Wherever that derivative, y', is zero, the curve is horizontal
This is twice at x = 1 and at x =2 and at x = 4

Look at the second derivative to see what happens there.
y'=(x-1)^2 (x^2-6x+8)
so
y" = (x-1)^2(2x-6)+2(x-1)(x^2-6x+8)
now what is y"at x = 1?
y"(1) = Zero, so that is an inflection point
what is y" at x = 2?
y"(2) = -2+0 = -2
That is a maximum because y" is negative
what is y"(4)?
y"(4) = 9(2)+2*3(16-24+8)
y"(4) = 18+0 = 18
so it is Minimum at x = 4
y"

## Similar Questions

1. ### how to sketch a graph of..

Local minimum and local maximum imply that the function approaches negative and positive infinite at opposite sides of the graph. Local minimum (1,1) and local maximum (3,3) means the slope of the function is 0 at these points. Thank …
2. ### Calc

1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)<0 if x<4 f'(4)=0 …
3. ### Math

When you're finding the sign of f' and f'' to find a local maximum/minimum, concavity and inflection point where do you substitute the tangent/critical points?
4. ### Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a …
5. ### calculus

a function has a local maximum at x=-2 and x=6 and a local minimum at x=1. how do u find the concavity of this function and point of inflection?
6. ### calculus

a function has a local maximum at x=-2 and x=6 and a local minimum at x=1. how do u find the concavity of this function and point of inflection?
7. ### Math

The derivative of a function is f'(x)=x(x+2)(x-5). Find the value of x at each point where f has a (a) local maximum, (b) local minimum, or (c) point of inflection