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Tanzania [10]
3 years ago
8

Consider the functions f(x)=3x squared - 5 and g(x)= square root of x -5 +2

Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0
F(5) = 3x(5)^2 - 5 = 3x25 - 5 = 75 - 5 = 70;
f(4) = 3x(4)^2 - 5 = 3x16 - 5 = 48 - 5 = 43;
f(x) + g(x) = 3x^{2} -5 + \sqrt{x-5} +2 = x^{2} + \sqrt{x-5} -3.
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The function y = x 2 - 10x + 31 has a ____
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Answer:

Option B. minimum is correct for the first blank

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Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

f(x) = x^2-10x+31

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Now the first derivative has to be put equal to zero to find the critical value

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The function has only one critical value which is 5.

Taking 2nd derivative

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As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

f(5) = (5)^2-10(5)+31\\=25-50+31\\=6

Hence,

<u>The function y = x 2 - 10x + 31 has a minimum  value of 6</u>

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

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