SOLUTION: Find the critical points of the following function. f(x)=2x^2-3x-5

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Question 1155422: Find the critical points of the following function.
f(x)=2x^2-3x-5
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Suppose that x=c is a critical point of .
If 'to the left of and ' to the right of , then is a local .
If 'to the left of and ' to the right of , then is a local .
If ' is the on both sides of then is neither a local maximum nor a local minimum.

.....derivate
'

-> a critical point: minimum
domain of is
(,)
is monotone in intervals:
-> is decreasing
-> is increasing








minimum is at: (,)

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Find the critical points of the following function.
f(x)=2x^2-3x-5
There are 3 CRITICAL points of a parabola. They are:

1) the y-intercept (it's obvious that this is - 5)

2) the x-intercepts, if any [solving the equation for x, by setting f(x) = 0 will accomplish this task, and also, this equation can be FACTORED]

3) the VERTEX (this is found by determining the x-coordinate of the vertex, using the formula: , and then substituting this x-value into f(x)

   to get the y-coordinate of the vertex. These 2 coordinates will give you the vertex of the parabola, which by the way is a MINIMUM, as indicated by the

   leading coefficient being > 0. Alternatively, you can convert the function to the vertex form of a parabola, but that may be too much work! 

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