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sashaice [31]
2 years ago
10

Find the vertex. f(x) = 9x2 + 1​

Mathematics
1 answer:
lidiya [134]2 years ago
4 0

Answer:

vertex = (0, 1 )

Step-by-step explanation:

f(x) = 9x² + 1 ← has it's vertex on the y- axis

let x = 0 in f(x)

f(0) = 9(0)² + 1 = 0 + 1 = 1

vertex = (0, 1 )

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Find the linear approximation of the function g(x) = 3 root 1 + x at a = 0. g(x). Use it to approximate the numbers 3 root 0.95
Virty [35]

Answer:

L(x)=1+\dfrac{1}{3}x

\sqrt[3]{0.95} \approx 0.9833

\sqrt[3]{1.1} \approx 1.0333

Step-by-step explanation:

Given the function: g(x)=\sqrt[3]{1+x}

We are to determine the linear approximation of the function g(x) at a = 0.

Linear Approximating Polynomial,L(x)=f(a)+f'(a)(x-a)

a=0

g(0)=\sqrt[3]{1+0}=1

g'(x)=\frac{1}{3}(1+x)^{-2/3} \\g'(0)=\frac{1}{3}(1+0)^{-2/3}=\frac{1}{3}

Therefore:

L(x)=1+\frac{1}{3}(x-0)\\\\$The linear approximating polynomial of g(x) is:$\\\\L(x)=1+\dfrac{1}{3}x

(b)\sqrt[3]{0.95}= \sqrt[3]{1-0.05}

When x = - 0.05

L(-0.05)=1+\dfrac{1}{3}(-0.05)=0.9833

\sqrt[3]{0.95} \approx 0.9833

(c)

(b)\sqrt[3]{1.1}= \sqrt[3]{1+0.1}

When x = 0.1

L(1.1)=1+\dfrac{1}{3}(0.1)=1.0333

\sqrt[3]{1.1} \approx 1.0333

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3 years ago
Fran brings home $225 per week working 15 hours of which she is able to save $40. Fran wants to have $1,400 saved at the end of
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Answer:

225+40+1,400=?

Step-by-step explanation:

8 0
3 years ago
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M is the slope and b is the y-intercept in the form
.. y = mx +b
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Matching patterns, you see that
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