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erica [24]
3 years ago
9

Find the local maximum and two local minima of the graph of the following function.

Mathematics
1 answer:
Archy [21]3 years ago
5 0

Answer:

max is (3, 1) and min are (2, 0) and (4, 0)

Step-by-step explanation:

Since there is no bounds on this (not a closed interval), the only max and min we can find are local.  The max and min points exist where the first derivative of the function is equal to 0.  That means that we have to find the first derivative.  That is:

y'=4x^3-36x^2+104x-96

If you factor this higher-degree polynomial (I used the Rational Root Theorem and then synthetic division), you find that the zeros of the derivative exist at the x values of

2, 3, 4

Therefore, f(2), f(3), and f(4) will either be max values or min values.

f(2) = 0 so the point is (2, 0)

f(3) = 1 so the point is (3, 1)

f(4) = 0 so the point is (4, 0)

As you can see, the max point is (3, 1)

the min points are (2, 0) and (4, 0)

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C. 3.50

Step-by-step explanation:

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3 years ago
H(t) = −t2 + t + 1 h(x + 1)
Harman [31]

The value of the function h(x + 1) is -x^2 - x + 1

<h3>How to evaluate the function?</h3>

The equation of the function is given as:

h(t) =-t^2 + t + 1

The function is given as:

h(x + 1)

This means that t = x + 1

So, we substitute t = x + 1 in the equation h(t) =-t^2 + t + 1

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Evaluate the exponent

h(x + 1) =-(x^2 + 2x + 1) + x + 1 + 1

Expand the brackets

h(x + 1) = -x^2 - 2x - 1 + x + 1 + 1

Evaluate the like terms

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Hence, the value of the function h(x + 1) is -x^2 - x + 1

Read more about functions at:

brainly.com/question/1415456

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<u>Complete question</u>

Consider the following function definition, and calculate the value of the function

h(t) = −t2 + t + 1 h(x + 1)

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1 year ago
Samantha bought 10 identical shirts for $25. If she bought 25 of those same shirts, how much will she pay?
tatiyna

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Step-by-step explanation:

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2 years ago
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Help me please !!!!! ASAP !
irga5000 [103]

Answer:

x = 6 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

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Subtract 36 from each side

x^2 = 144-36

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