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Find the minimum value of 2x^2 - 10x + 15.

 May 31, 2020
 #1
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You must minimise the function. To do this, you must allow the derivative of the function to be equal to zero:

 

\(f(x) = 2x^2 -10x + 15\)

\(f'(x) = 4x - 10\)

 

Now let the fucntion equal zero and find the value of x at this point:

 

\(0 = 4x - 10\)

\(10 = 4x\)

\(10/4 = 2.5 = x\)

 

Sub this back into the initial function to find the lowest point of this parabola:

 

\(f(2.5) = 2(2.5)^2 - 10(2.5) + 15\)

 

This coincidentally comes to a minimum of 2.5

Hope this is right :)

 May 31, 2020

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