How do you find the important points to graph #f(x)= -x^2-4x#?

Answer 1

Check below for detail examination of the function.

#f(x)=-x^2-4x# ,
#D_f=RR#

#f(x)=0 <=> -x^2-4x=0 <=> x^2+4x=0 <=> x(x+4)=0 <=> (x=0, x=-4)#

#f'(x)=-2x-4=-2(x+2)#

#f'(x)=0# #<=> x=-2#

#f''(x)=-2<0#
#x##in##RR#

  • We get these tables for monotony and concavity of #f#:

#f# has global maximum at #x_0=-2# , #f(-2)=4#

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Answer 2

To graph the function ( f(x) = -x^2 - 4x ), you can follow these steps:

  1. Identify the vertex of the parabola using the formula ( x = -\frac{b}{2a} ) where ( a = -1 ) and ( b = -4 ).
  2. Substitute the value of ( x ) obtained from step 1 into the function to find the corresponding ( y )-coordinate.
  3. Determine the ( x )-intercepts by solving the equation ( -x^2 - 4x = 0 ) for ( x ).
  4. Plot the vertex, ( x )-intercepts, and any additional points if needed.
  5. Draw the parabola passing through these points.

This process will help you find the important points to graph the given function.

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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.

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.

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.

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.

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