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erica [24]
3 years ago
13

If​ f(x) and​ g(x) are differentiable functions such that f (1 )equals 4​, f prime (1 )equals 5​, f prime (9 )equals 6​, g (1 )e

quals 9​, g prime (1 )equals 8​, g prime (2 )equals 9​, g prime (5 )equals 10​, find StartFraction d Over dx EndFraction f (g (x ))vertical line Subscript x equals 1 Superscript .
Mathematics
1 answer:
Alex777 [14]3 years ago
8 0

By the chain rule,

(f(g(x)))'=f'(g(x))g'(x)

so that when x=1, we have

(f(g(1)))'=f'(g(1))g'(1)=f'(9)g'(1)=6\cdot8=\boxed{48}

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The table below represents a linear function f(x) and the equation represents a function g(x):
Elza [17]

Answer:

(a) The slope of f(x) is greater than the slope of g(x)

(b) f(x) has a greater y intercept

Step-by-step explanation:

Given

\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}

g(x) = 3x - 2

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

This gives:

m = \frac{f(0) - f(1)}{0 - 1}

m = \frac{f(0) - f(1)}{- 1}

Substitute values for f(0) and f(1)

m = \frac{-1 - 7}{- 1}

m = \frac{-8}{- 1}

m = 8

The slope of g(x) can be gotten using the following comparison

g(x) = mx + b

m \to slope

So:

g(x) = 3x -2

m = 3

m_{f(x)} > m_{g(x)}

Solving (b): Compare the y intercept

y intercept is when x = 0

From the table of f(x)

f(0) = -1

From the equation of g(x)

g(x) = 3x -2

g(0) = 3*0-2

g(0) =-2

<em></em>f(0) > g(0)<em></em>

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3 years ago
3. Find the slope between the two points (-3,3) and (3,-1) Your Answer:​
WARRIOR [948]
The slope is -2/3 I hope this helped
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Answer:

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Step-by-step explanation:

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The graph of y=-3x+4 is:
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y=-3x+4

this is a line with slope -3 and y intercept of 4

the line is all the points that are the solutions to the equation

D.a line that shows the set of all solutions to the equation


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