What is the vertex of # y=x^2/7-7x+1 #?
check if this point is of maximum or minimum by second derivative test(thisstep is not necessarily needed) if second derivative is -ve it corresponds to point of maximum if second derivative is +ve it corresponds to point of minimum
graph{x^2/7-7x+1 [-10, 10, -5, 5]}
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The vertex of the function ( y = \frac{x^2}{7} - 7x + 1 ) can be found using the formula for the x-coordinate of the vertex, which is given by ( x = -\frac{b}{2a} ) in the standard form of a quadratic function ( y = ax^2 + bx + c ). In this case, ( a = \frac{1}{7} ) and ( b = -7 ). Plugging these values into the formula, we get:
( x = -\frac{(-7)}{2 \cdot \frac{1}{7}} )
Simplifying further:
( x = -\frac{-7}{\frac{2}{7}} )
( x = -\frac{-49}{2} )
( x = \frac{49}{2} )
Now, substitute this value of ( x ) into the original function to find the corresponding y-coordinate:
( y = \frac{(\frac{49}{2})^2}{7} - 7(\frac{49}{2}) + 1 )
( y = \frac{2401}{28} - \frac{343}{2} + 1 )
( y = 85.75 )
So, the vertex of the function is ( \left(\frac{49}{2}, 85.75\right) ).
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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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