Determine whether the function f(x)=-x2+4x has a minimum or maximum value?

Question

The problem is f(x) -x (squared) +4x

The choices for the answer are:

minimun
maxiumum
neither
cannot be determined

Answer 1

The derivative is -2x + 4
Setting that equal to zero gives you 2 as the critical number
Subbing 2 into the original equation gives you a corresponding y coordinate of 4. So you know you have a relative extrema at (2,4)

All you need to figure out is whether it's a maximum or a minimum. Draw a line and label the number 2 in the middle. Pick a number to the left of two (say 1) and sub it into the equation of the derivative, it gives you a positive sign (-2(1)+4=2)

Do the same for a number to the right of 2 (say 3). It gives you a negative number for an answer. (-2(3)+4=-2)

According to the first derivative test, when f prime at x changes from positive to negative at c (our critical number which is 2), then f(c) or f(2) in our case is a relative maximum of f. That means at (2,4) we get our maximum and therefore the maximum is four and to answer your question, the function has a maximum.

Answer 2

question style a million : For this function y(x)= -4*x^2 + 8*x + 3 , answer right here questions : A. locate the minimum/optimum factor of the function ! answer style a million : The equation -4*x^2 + 8*x + 3 = 0 is already in a*x^2+b*x+c=0 form. via matching the consistent place, we are in a position to derive that the linked fee of a = -4, b = 8, c = 3. 1A. locate the minimum/optimum factor of the function ! because of the fact the linked fee of a = -4 is unfavourable, the function y(x) = -4*x^2 + 8*x + 3 have a optimum factor. to locate the optimum factor use the formula y'(x) = 0 , to locate the linked fee of x we ought to consistently locate the function y'(x) first So we get y'(x) = - 8*x + 8 = 0 this ability that -8*x = -8 this ability that x = -8/-8 So we get x = a million So the optimum factor is ( x , y ) = ( a million , y(a million) ) this is ( x , y ) = ( a million , 7 ) So the optimum fee is 7

Answer 3

Just think about what the graph would look like.

You know an x^2 graph is a parabola, and that adding a negative in front of the x^2 will flip it upside down. If a parabola has a low point, which is the minimum. If that parabola is flipped upside down, it will now have a high point, a maximum.

Answer 4

It has a maximum for x=2.

You can find that either with the standard formula for quadratic curves or by taking the derivative.

y = a*x^2 + b*x + c has a minimum/maximum at -b/2a
if a < 0 then it's a maximum, if >0 then minimum.

Answer 5

It's a parabola, right? Since the sign in front of x² is negative, does the parabola open up or down? And if it opens up, would there be a minimum or a maximum? What if it opens down?