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topjm [15]
2 years ago
15

Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10

Mathematics
1 answer:
Diano4ka-milaya [45]2 years ago
4 0

Hello,

Step-by-step explanation:

f(x) = ln(x) {}^{4}

(ln(u)') =  \frac{u'}{u}

f'(x) =  \frac{4ln {}^{} (x) {}^{3} }{x}

f'(10) =  \frac{4ln {}^{} (10) {}^{3} }{10}  =  \frac{12ln(x)}{x}

f(10) = ln(10) {}^{4}

y =  \frac{12ln(x)}{x} (x - 10) + 4ln(10)

y = f'(a)(x - a) + f(a)

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Let's make the length L and the width w. So, here's what we know:

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2 years ago
Given g(x) = −3x + 4
Goshia [24]

Answer:

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Step-by-step explanation:

We are given the function:

g(x) = -3x + 4

And we want to determine its average rate of change of the function for <em>x</em> = <em>a</em> and <em>x</em> = <em>a</em> + <em>h</em>.

To determine the average rate of change, we find the slope of the function between the two points. In other words:

\displaystyle \text{Avg} = \frac{g(a + h) - g(a) }{(a + h ) - a}

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\displaystyle \begin{aligned}  \text{Avg} &= \frac{g(a + h) - g(a) }{(a + h ) - a} \\ \\ &=\frac{(-3(a+h) + 4) - (-3a+4)}{h} \\ \\ &= \frac{(-3a -3h + 4) + (3a - 4) }{h} \\ \\ &= \frac{-3h}{h} \\ \\ &= -3\end{aligned}

In conclusion, the average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to <em>x</em> = <em>a</em> + <em>h</em> is -3.

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