How do I figure out the maximum or minimum value of f(x)=2x^2+7x+3?

At maximum or minimum values, the gradient is 0.





Therefore, f(x) = 0.





Solve the equation 0=2x^2+7x+3





You should get one or two values for x.





Substitute these values into the equation of the line, and theres your points.How do I figure out the maximum or minimum value of f(x)=2x^2+7x+3?
a) draw the curve on a piece of paper


b) since the curve is open at the top it has only a minimum





How to find a minimum??


a) a minimum occurs with this type of curve when the slope = 0


b) to find the slope derive f(x)=2x^2+7x+3


f'(x) = 4x + 7


for which value of x, 4x + 7=0


and you are done.





How do I figure out the maximum or minimum value of f(x)=2x^2+7x+3?
find the value of x when





df(x)/dx=0





then sub that into





d^2f(x)/dx^2





if that comes out neagtive its a max, if positive its a min





hope that helps