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Nata [24]
3 years ago
7

This question is about finding the slope of the tangent line to an inverse function. I would love to know if my answer of 1/5 is

correct.
g(1) = 2
g^-1(2) = 1

(g^-1(x))' = 1/(g'(g-1(x))
(g^-1(2))' = 1/g'(g-1(2))
(g^-1(2))' = 1/g'(1)

g(x) = x^3 + 2x - 1
g'(x) = 3x^2 + 2
g'(1) = 3+2=5
(g^-1(2))' = 1/5

Mathematics
1 answer:
Nikolay [14]3 years ago
7 0
Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.

Here's another way to look at it:

When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.

For any tangent on g(x), its slope is m = (dy)/(dx)

The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here. 

So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.
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Answer:

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4 0
3 years ago
.......…............
Nookie1986 [14]

Answer:

\frac{7}{8} \div \frac{1}{2} = \frac{7}{4}

Step-by-step explanation:

Here we are given four equations and we have to find the equation that gives the number of half inches that are in \frac{7}{8} inches.

To find how many half inches i.e. \frac{1}{2} inches are there in \frac{7}{8} inches we have to divide \frac{7}{8} by \frac{1}{2}.

So, the equation that will give the result is \frac{7}{8} \div \frac{1}{2} = \frac{7}{8} \times \frac{2}{1} = \frac{7}{4} (Answer)

6 0
2 years ago
Help please due now!
MissTica

Answer:

8

Step-by-step explanation:

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6 0
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