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Vladimir79 [104]
2 years ago
7

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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3 years ago
Find the equation of a circle with a center at (–7, –1) where a point on the circle is (–4, 3).
gogolik [260]

Answer:

(x + 7)^2 + (y + 1)^2 = 25.

Step-by-step explanation:

The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.

In this case, a = -7 and b = -1, so we have...

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To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.

sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.

Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.

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8 0
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