maxima and minima

Hi currently got this question,

Locate the co-ordinates of the turning point for the following function and determine whether it is a maxima or minima.

Y=7x²-3x
Now i believe my working out is correct but i dont know if this gives me a max or minima or am i missing another step thanks

Let y’=0 and find values for x

Y’=14x-3

Y’’= 14+0=y’’(x)=14

Looking for turn points by finding the roots of the derivative

14x-3=0

14x=3

X=0.2142857143

Reply 1

m184

substitute the x coordinate of your turning point into the second derivative. you will know if it is a maximum point or minimum depending on if the answer is less or greater than 0

Reply 2

Scott-92

Original post by m184

substitute the x coordinate of your turning point into the second derivative. you will know if it is a maximum point or minimum depending on if the answer is less or greater than 0

Just make sure im getting it. My second derivative being x=14? thanks

Reply 3

m184

Original post by Scott-92

Just make sure im getting it. My second derivative being x=14? thanks

yeah that looks right

Reply 4

Kallisto

Entertainment Forum Helper

Derive the funcion twice, equal the first derivation to zero:

Y' = 0

Determine the x value and put it in the second derivation. If

Y'' < 0, it is a maximum at this x value
Y'' > 0, it is a mimimum at this x value

Put the x value in the original function Y to get the y value and thus the point of the maximum or minimum.