Question

the curve represents the titration of 100.0 ml of a naoh solution (in the flask) with a solution of 0.20 m hcl (in the burette). determine the concentration of the naoh solution from the information provided on the graph.

Answer 1

The below graph is proved.

What is graph?

graph is a mathematical representation of  a network and it describes the relation between lines and points.

The degree of f(z) is 7

Part B

The leading coeffient negetive?

There are 5 distinct real zeros and 2 relative minimum values.

From the of a polynomial from a graph of the polynomial, starting from the left, we have;

1) The graph touches the x-axis (horizontally) and then crosses, which gives a multiplicity of 3

2) The graph crosses the x-axis once going upwards with a multiplicity of 1

3) Next, the graph crosses the x-axis once going downwards with a multiplicity of 1

4) Next, the graph crosses the x-axis once going upwards with a multiplicity of 1

5) Finally, the graph crosses the x-axis once going downwards with a multiplicity of 1

Part A

The degree of f(x) is therefore, 3 + 1 + 1 + 1 + 1 = 7

Part B

The leading coefficient negative of a polynomial that has an odd degree power with a graph falls to the right and rises to the left, the leading coefficient is negative;

Part C

The number of zeros = 7 zeros

The number of identical zeros = 3 identical zeros

∴ The number of distinct zeros are 7 zeros - 2 identical zeros = 5 distinct zeros

The graph continues from +∞ to -∞, therefore, the number relative minimum value of the polynomial are the two minimum values

The number of relative minimum values = 2

Thus ,there are 5 real distinct zeros and 2 relative minimum values.

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