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How do you find the maximum or minimum of #f(x)=x^2+6x-2#?

Answer 1

Isaiah Allen

#"minimum at "(-3,-11)#

differentiate f(x) and equate to zero.

#rArrf'(x)=2x+6#

#2x+6=0rArrx=-3#

#rArrf(-3)=9-18-2=-11#

#rArr" stationary point at " (-3,-11)#

Using the #color(blue)"second derivative test"#

• If f'' (a) > 0 then minimum

• If f'' (a) > 0 then maximum

#rArrf''(x)=2>0tocolor(red)"minimum"# graph{x^2+6x-2 [-40, 40, -20, 20]}

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Answer 2

Emily Ammerman

To find the maximum or minimum of ( f(x) = x^2 + 6x - 2 ), follow these steps:

Find the derivative ( f'(x) ) of the function.
Set ( f'(x) = 0 ) and solve for ( x ) to find critical points.
Use the second derivative test or analyze the behavior of the function around critical points to determine whether each critical point corresponds to a maximum or minimum.
If the second derivative test is inconclusive, you may need to consider additional methods, such as evaluating the function at endpoints of a given interval or using other techniques.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.