# Algebra

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f(x) = – x^2 + 10x – 26. Determine whether there is a maximum or
minimum value and find that value.

• Algebra -

This is algebra?

If you have not learned differentiation, perhaps your teacher wants you to use a calculator to find the extrema. (If you have, disregard this paragraph).

Take the derivative of f(x):
f'(x)= -2x + 10

Set f'(x) = 0
-2x + 10 = 0
10 = 2x
x = 5

Now use a sign line to find whether x=5 is a minimum or maximum.

f'(0) = +
f'(10) = -

x=5 is a maximum because f'(x) changes signs from + to -

• Algebra -

complete the square,
f(x) = – x^2 + 10x – 26
= - [x^2 - 10x + 25 - 25] - 26
= -(x-5)^2 + 25 - 26
= -(x-5)^2 - 1

so the vertex is (5,-1) and since the parabola opens downwards, it will be a maximum point and the maximum value of the function is -1

• Algebra -

I do not think these answers are right. I get somethin else and 5 is not an option. Here are the choices

A. Minimum is 25
B. Minimum is -51
C. Maximum is -1
D. Maximum us -51

• Algebra -

5 is the value at which the maximum occurs. f(5) = -1, so choice C.

• Algebra -

I was thinking that as well! Thanks!

• Algebra -

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