Determine wether the given quadratic function has a maximum or minimum value and then find the value.?

Question

f(x) = 4x^2 - 4x
minimum value; -1
maximum value; 1
minimum value; -3
maximum value; 3

Answer 1

I'm not sure what the two pairs of max/min values in your equation are supposed to represent. The simple calculus method for finding max/min values works like this:

f'(x)=8x-4=0 take derivative with respect to x, and set = to 0

8x=4
x=.5 solve

f''(x)=8 take second derivative, since it is is positive, the value is a minimum

plug into equation f(.5)=4(.5)^2 -4(.5) = -1

keep at it
math is good stuff

Answer 2

question type a million : For this function y(x)= -x^2 + 2*x - 4 , answer proper right here questions : A. locate the minimum/optimal aspect of the function ! answer type a million : The equation -x^2 + 2*x - 4 = 0 is already in a*x^2+b*x+c=0 sort. by matching the consistent position, we may be able to derive that the fee of a = -a million, b = 2, c = -4. 1A. locate the minimum/optimal aspect of the function ! because the fee of a = -a million is unfavourable, the function y(x) = -x^2 + 2*x - 4 have a optimal aspect. in view that optimal aspect is the position the curve turn, so the formula y'(x) = 0 , can be utilized to locate the fee of x we ought to locate the function y'(x) first So we get y'(x) = - 2*x + 2 = 0 which signifies that -2*x = -2 which signifies that x = -2/-2 So we get x = a million So the optimal aspect is ( x , y ) = ( a million , y(a million) ) this is ( x , y ) = ( a million , -3 ) So the answer is B Max (a million,-3)

Answer 3

Because the coefficient before the x^2>0, it has a minimum value, which would be according to the formula b/2a, which is -4/2(4)= -4/8= -1/2

so it would be a minimum value of -.5

Answer 4

Take the first derivative, so it's 8x -4, set to 0, solve, gives you 2, sub into 4x^2 -4x, gives you 8, that's the absolute mac, for the mins check the endpoints of your region. I couldnt understand what you meant by the multiple constraints. Maybe one set refers to y's?

Answer 5

f(x) = 4x^2 - 4x

x = (-b/2a)

x = (-(-4))/(2(4))
x = 4/8
x = (1/2)

f(1/2) = 4(1/2)^2 - 4(1/2)
f(1/2) = 4(1/4) - 2
f(1/2) = 1 - 2
f(1/2) = -1

Minimum Value of -1

Answer 6

you hve to do the 2nd derivative

Answer 7

maximum; -1

Just use a graphic calculator.