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Andrei [34K]
4 years ago
6

Property for 5x +15=-4

Mathematics
1 answer:
erastova [34]4 years ago
4 0

5x +15=-4 5x=-4-15 5x=-20 X=-20/5 X=-4

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(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivativ
svetlana [45]

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

\mathbf{h(x) = f(g(x))}

Start by calculating the equations of f(x) and g(x)

<u>Graph f(x)</u>

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}

\mathbf{f(x) = -\frac{3}{2}x,\  x \ge 2}

<u>Graph g(x)</u>

The slope of g(x) is: -1/2

So, the equation is:

\mathbf{g(x) = -\frac 12x}

<u>For x = 1 and x = 2, we have:</u>

So, we have:

\mathbf{h(x) = f(g(x))}

Where:

\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2} and \mathbf{g(x) = -\frac 12x}

\mathbf{h(x) = f(g(x))} becomes

\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}

Open brackets

\mathbf{h(x) = -\frac{3}{4}x}

Differentiate

\mathbf{h'(x) = -\frac{3}{4}}

So:

\mathbf{h'(1) = -\frac{3}{4}}

\mathbf{h'(2) = -\frac{3}{4}}

For x = 3, we have:

\mathbf{h(x) = f(g(x))}

Where:

\mathbf{f(x) = -\frac{3}{2}x\  x \ge 2} and \mathbf{g(x) = -\frac 12x}

\mathbf{h(x) = f(g(x))} becomes

\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}

\mathbf{h(x) = \frac{3}{4}x}

Differentiate

\mathbf{h'(x) = \frac{3}{4}}

Substitute 3 for x

\mathbf{h'(3) = \frac{3}{4}}

Hence, the values of the derivatives are:

\mathbf{h'(1) = -\frac{3}{4}}, \mathbf{h'(2) = -\frac{3}{4}} and \mathbf{h'(3) = \frac{3}{4}}

Read more about graphed functions at:

brainly.com/question/11804653

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Any help is apprenticed!
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