Question

Please help on Minimum and Maximum question

Determine the minimum and maximum values of f(x)=-4(x-6)^2+3 and the graph of g(x)=2cos(2*x-pi)+4

Answer 1

f(x)=-4(x-6)^2+3.. x = 6 and g(x)=2cos(2*x-pi)+4 aplitude: 2. Period: pi. Phase shift pi/2. Hope it helped a little
Medel please :)

Answer 2

How do you find the Min and Max for these functions though?

Answer 3

for the first one the turning point is at (-6,3) and since the coefficient of x^2 is negative this is a maximum maxm of the function = 3.
There is no minimum value as its a parabola which opens downwards.

Answer 4

% turning point is at (6,3)

Answer 5

this is the graph for the second equation

Answer 6

Yes
So you just have to read off the maxm and minm from the graph.

Answer 7

So Maximum would be 6 and Minimum would be 2?

Answer 8

exactly

Answer 9

and is there an equation to determine the min and max of a function?

Answer 10

no Not one equation fits all.

For a parabola you write the equation in vertex form - as in your question.

For a trig function you can either draw the graph or work it out from the amplitude and displacement in some cases.

Answer 11

Or you can use calculus - have you done any calculus yet?

Answer 12

finnding derivatives?

Answer 13

I'm in pre-calc this year

Answer 14

oh ok

Answer 15

But I'm not very confident in finding derivatives

Answer 16

I#ll see if i can find a good website for you

Answer 17

Thanks

Answer 18

https://www.mathsisfun.com/calculus/derivatives-rules.html

that one summarises it pretty well.
When finding maxm and manm you find the derivative of the function and equate it to 0.
This will give you the x value of the turning point.
One way to find it its a maxm or minm is to find the second derivative and check its sign.

Answer 19

Thanks!

Answer 20

so for f(x) = -4(x - 6)^2 + 3
derivative = f'(x) = -4*2(x - 6) = 0
-8x + 48 = 0
x = 6

So the turning point of the graph is where x = 6

to find value of f(x) when x = 6 plug x=6 into f(x) - this gives you 3
so turning point when f(x) = 3

to find if this is a maxm or minm find second derivative

f'(x) = -8(x - 6) = -8x + 48
Second derivative
f" (x) = -8 which is negative so this means f(x) = 3 is a maxm

( negative second derivative would be a minm)

and as there is only one value of send derivative there is no minimum

Answer 21

This is my first time using open study so how do I give you a medal

Answer 22

click on the blue box Best Response

Answer 23

Make the most of OS - it closes on Jan 31 2017 Im afraid.

Answer 24

why is it closing?

Answer 25

Basically Money

Answer 26

Oh I believe it

Answer 27

Well thank you for the help!