Let f(x)=x2−8x+19 What is the minimum value of the function?
2 answers:
In order to find the minimum value or the 'vertex' in this case, we need to take the first derivative and second derivative.
The first derivative informs us of stationary points. Because this is a quadratic, there should be a point where the curve comes back up.
The second derivative determines the concavity of the stationary point. If the second derivative is less than zero, there lies a maximum turning point (ie a maximum value), and if the second derivative is greater than zero, there lies a minimum turning point (ie a minimum value).
Now, we let the first derivative equal to zero, because that's when we have the tip of the slope or the horizontal tangent of the parabola.
So, we know there is a horizontal tangent at x = 4.
Let's make sure this is a minimum value.
Since the second derivative is greater than zero, there lies a minimum value at x = 4.
Hence, the minimum value of the function is x = 4
The first derivative informs us of stationary points. Because this is a quadratic, there should be a point where the curve comes back up.
The second derivative determines the concavity of the stationary point. If the second derivative is less than zero, there lies a maximum turning point (ie a maximum value), and if the second derivative is greater than zero, there lies a minimum turning point (ie a minimum value).
Now, we let the first derivative equal to zero, because that's when we have the tip of the slope or the horizontal tangent of the parabola.
So, we know there is a horizontal tangent at x = 4.
Let's make sure this is a minimum value.
Since the second derivative is greater than zero, there lies a minimum value at x = 4.
Hence, the minimum value of the function is x = 4
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Answer:
Or if you want with the value of h too.
Step-by-step explanation:
Find the value of h and k by using the formula.
From y = x²-2
Substitute these values in the formula.
Therefore, h = 0.
Therefore, k = - 2.
From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.
These type of equation where b = 0 can also be both standard and vertex form.
Lets remember the property "alternative-interior angles" when we have parallels lines:
Given two paralles lines, the following is true:
In our question, we have:
We know that the angles J + P + K=180
So, the triangles have all the angles the same, so they are similar by angle-angle-angle, and they have one side congruent, AC=CD, so the triangles are congruents.
