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2 years ago

The graph of function f is shown above. if g(x)=x^2/f(x) what is the value of g'(1)?

Mathematics

1 answer:

Alla [95]2 years ago

7 0

Answer:

Step-by-step explanation:

Find the equation of the segment going from (0,-5) to (3,7)

y intercept = -5

Slope = (-5 - 7) / (0 - 3) = -12/-3 = 4

equation: y = 4x - 5

g(x) = x^2 / f(x)

f(x)= (4x - 5)

g(x) = x^2 / (4x - 5)

g'(x) = x^2 * (4x - 5)^-1

g'(x) = 2x*(4x - 5)^-1 + (-1) *4* x^2 (4x - 5)^-2

I will leave that monster the way it is and just find g'(1)

g'(1) = 2(1) * (4(1) - 5)^-1 + (-1) (1)^2 *4* (4(1) - 5)^-2

g'(1) = 2(1) * (-1)^-1 + (-1) (1)^2 *4 * (-1)^2

g'(1) = -2 + (-1) (1)^2 (4)

g'(1) = - 2 + (-1) (1)^2 (4)

g'(1) = - 2 - 4

g'(1) = - 6

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40 inches

Step-by-step explanation:

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2 years ago

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3 years ago

Which function is f(x) equal to f^-1(x)?

Morgarella [4.7K]

Answer:

c. f(x) x+1/x-1

Step-by-step explanation:

To answer this question, we need to check each answer one by one until we find the right one.

y = (x+6)/(x-6)

switch x and y

x = (y+6)/(y-6)

solve for y

x(y-6) = y+6

xy - 6x = y+6

y(x-1) = 6x+6

y = (6x+6) /(x-1) = 6(x+1)/(x-1)

f^-1(x) = 6(x+1)/(x-1)

y = (x+2)/(x-2)

switch x and y

x = (y+2)/(y-2)

solve for y

x(y-2) = y+2

xy -2x = y+2

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y = (x+1)/(x-1) ------ correct one

switch x and y

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x(y-1) = y+1

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6 0

3 years ago

Read 2 more answers

Can you add a negative and a positive when doing like term

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5 0

3 years ago

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The children in my subdivision were bored one summer and decided to hold a competition to see who could run to the end of the st

Ainat [17]

Answer:

6.7% of children who finished the race in under 45 seconds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 75 seconds

Standard Deviation, σ = 20 seconds

We are given that the distribution of time of completion is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(finished the race in under 45 seconds.)

P(x < 45)

$P( x < 45) = P( z < \displaystyle\frac{45 - 75}{20}) = P(z < -1.5)$

Calculation the value from standard normal z table, we have,

$P(x < 45) = 0.067 = 6.7\%$

6.7% of children who finished the race in under 45 seconds.

4 0

3 years ago

The graph of function f is shown above. if g(x)=x^2/f(x) what is the value of g'(1)?​

The graph of function f is shown above. if g(x)=x^2/f(x) what is the value of g'(1)?