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2 years ago

Determine whether the statement is true or false. If f '(c) = 0, then f has a local maximum or minimum at c.

Physics

1 answer:

ankoles [38]2 years ago

4 0

It is False that, If f '(c) = 0, then f has a local maximum or minimum at c.

Local maximum and minimum points are very distinctive on the graph of a function and are thus, helpful in grasping the shape of the graph. Either a local minimum or a local maximum can be considered a local extremum.

A counterexample can be used for:

f(x) = x³

f'(x) = 2 × x²

and,

f'(0) = 2×0² = 0

However, the assertion is false because x = 0 is actually an inflection point rather than a maximum or minimum in f(x) = x³.

Know more about f(x) here: brainly.com/question/28058540

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A square is 1.0 m on a side. Point charges of +4.0 μC are placed in two diagonally opposite corners. In the other two corners ar

finlep [7]

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Explanation:

<u>Electric Potential Due To Point Charges </u>

The electric potential produced from a point charge Q at a distance r from the charge is

$\displaystyle V=k\frac{Q}{r}$

The total electric potential for a system of point charges is equal to the sum of their individual potentials. This is a scalar sum, so direction is not relevant.

We must compute the total electric potential in the center of the square. We need to know the distance from all the corners to the center. The diagonal of the square is

$d=\sqrt2 a$

where a is the length of the side.

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$\displaystyle r=\frac{d}{2}=\frac{a}{\sqrt{2}}$

$\displaystyle r=\frac{1}{\sqrt{2}}=0.707\ m$

The total potential is

$V_t=V_1+V_2+V_3+V_4$

Where V1 and V2 are produced by the +4\mu C charges and V3 and V4 are produced by the two opposite charges of $\pm 3\mu\ C$ . Since all the distances are equal, and the charges producing V3 and V4 are opposite, V3 and V4 cancel each other. We only need to compute V1 or V2, since they are equal, but they won't cancel.