Question

Can someone tell me how to find local maxima and minima! (Please)

Answer 1

@ganeshie8

Answer 2

@jim_thompson5910

Answer 3

what's the function?

Answer 4

No in general for any function

Answer 5

Take any example

Answer 6

well you would derive the function f(x) to get f ' (x)

Answer 7

then set the derivative f ' (x) equal to zero

and solve for x to get a list of critical values

Answer 8

after you get a list of critical values, you have to use either the first derivative test or the second derivative test to see which critical value is a local min, local max, or a saddle point

Answer 9

Ok so
fo f(x) = 3t^2 - 4t
f ' = 6t - 4

I set that = 0
6t -4 =0
t = 4/6

After that

Answer 10

are you familiar with the first derivative test ?

Answer 11

No actually i want to learn that

Answer 12

I found out the first derivative

Answer 13

ok

Answer 14

draw out a number line and plot 4/6 on it

Answer 15

on either side of 4/6, plot a number

so 0 is on the left for instance and 1 is on the right

Answer 16

if you were to plug x = 0 into the derivative function, you get ???

Answer 17

-4

Answer 18

so we get a negative result when you plug in a number to the left of 4/6



We denote this with a negative sign circled above the interval (from negative infinity to 4/6)

Answer 19

what happens when you plug in x = 1 ?

Answer 20

2
Positive sign