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wel
3 years ago
6

Find (f^-1)'(7) without finding the inverse function where f(x) = 5 – 2x^3.

Mathematics
1 answer:
faltersainse [42]3 years ago
5 0

Step-by-step explanation:

the derivative of an inverse function is

1/f'(f^-1(x))

f'(x) = -6x²

f^-1(7) is solving the original function equation for x under the knowledge that y = 7

7 = 5 - 2x³

2 = -2x³

-1 = x³

=>

x = -1

f'(-1) = -6×(-1)² = -6×1 = -6

so,

(f^-1)'(7) = -1/6

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What is the rate of change between the interval x= pi and x= 3pi/2
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Answer:

\frac{6}{\pi } or 1.9099

Step-by-step explanation:

Look for y values at each of those given values of "x" and apply the slope formula.  When x = pi. y = -1 so the coordinate is (\pi,-1).  When x = 3pi/2, y = 2 so the coordinate is (\frac{3\pi }{2},2)

Plug those values into the slope formula:

\frac{2-(-1)}{\frac{3\pi }{2}-\pi}

You need a common denominator of pi:

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4 years ago
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3 years ago
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Answer:

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3 years ago
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Step-by-step explanation:

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8 0
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