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m_a_m_a [10]
2 years ago
12

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at

x = 1.
Mathematics
1 answer:
Amiraneli [1.4K]2 years ago
4 0

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

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the length of a rectangle is 2 inches longer than twice its width. If the area of the rectangle is 24 square inches, what are th
gregori [183]

Answer:

The length is 8 inches and the width is 3 inches

Step-by-step explanation:

Let w represent the width.

The length can be represented by 2w + 2

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A = lw

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Simplify and solve for w:

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w² + w - 12

Factor:

(w + 4)(w - 3)

Set equal to 0 and solve for each factor:

w + 4 = 0

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Since the width cannot be negative, the width has to be 3.

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7 0
3 years ago
What is 2 times 8/10???​
antiseptic1488 [7]

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5 0
2 years ago
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