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3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does not exist, enter DNE.)

Mathematics

1 answer:

vodka [1.7K]3 years ago

7 0

Answer:

absolute max is 120 and absolute min is -8

Step-by-step explanation:

Find critical numbers

f'(x) = 3x^2 - 12x + 9 = 0

= 3(x^2 - 4x + 3) = 0

3(x-3)(x-1) = 0

(x-3) = 0 or (x-1)=0

x = 1,3

Test them!

x<1 Sign of f' on this interval is positive

1<x<3 Sign of f' on this interval is negative

x>3 Sign of f' on this interval is positive

f(x) changes from positive to negative at x = 1 which means there is a relative maximum here.

f(x) changes from negative to positive at x = 3 which means there is a relative minimum here.

Test the endpoints to find the absolute max and min.

f(-1) = -8

f(1) = 12

f(3) = 8

f(7) = 120

The absolute maximum value of f is 120 and the absolute minimum value of f is -8.

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3 years ago

Make a table of values for f(x+2) given the graph

Salsk061 [2.6K]

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3 years ago

What the y-intercept of (8,0) and (3,7)

Anettt [7]

Answer:

$\sf \bf y - intercept = \dfrac{56}{5}$

Step-by-step explanation:

Y-intercept:

(8,0) ; x₁ = 8 & y₁ = 0

(3,7) ; x₂= 3 & y₂ = 7

First find the slope of the line.

$\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}$

$\sf = \dfrac{7 - 0}{3 - 8}\\\\ =\dfrac{7}{-5}\\\\=\dfrac{-7}{5}$

slope y-intercept form of the line: y = mx + b

Substitute the slope and x and y in the above equation. We can choose anyone of the given points.

$0 = \dfrac{-7}{5}*8 + b\\\\0=\dfrac{-56}{5}+b\\\\\dfrac{56}{5}=b\\\\ \boxed{\bf b = \dfrac{56}{5}}$

3 0

2 years ago

suppose that a water fountain produces a stream of water that follows the shape of a parabola. assigning the origin of a coordin

Readme [11.4K]

The quadratic regression equation for the stream of water is $y=-0.139x^{2} +1.667x$ {parabola}

Given that the water stream produced by fountain is parabola

Vertex of parabola is (6,5) , parbola is facing downward,axis of symmetry of parabola is x=6 and parabola passes through (0,0)

according to symmetry the third point on the parabola is (12,0)

General equation for a parabola⇒ Y=-4a $X^{2}$

⇒(y-5)=-4a $(x-6)^{2}$ { as the Vertex of parabola is (6,5) }

⇒(y-5)=-4a( $x^{2} +36-12x$ )

subtituting (0,0) in the equation to get the value of a

⇒-5=-4a(36)

⇒ a= $\frac{-5}{144}$

equation of parabola⇒(y-5)=-4( $\frac{5}{144}$ ) $(x-6)^{2}$

Therefore,The quadratic regression equation for the stream of water is $y=-0.139x^{2} +1.667x$

Learn more about parabola here:

brainly.com/question/21685473

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2 years ago

In right triangle PQR , PQ=12 cm and QR=5cm .What is cos R?

Juliette [100K]

Answer:

cosR = $\frac{5}{13}$

Step-by-step explanation:

assuming the right triangle has ∠ Q = 90° with legs 5 and 12

then this is a 5- 12- 13 right triangle with hypotenuse PR = 13 cm

then

cosR = $\frac{adjacent}{hypotenuse}$ = $\frac{QR}{PR}$ = $\frac{5}{13}$

7 0

2 years ago