Use calculus to find the absolute maximum and minimum values of the function. f(x) = 5x − 10 cos(x), −2 ≤ x ≤ 0 (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.

The absolute maximum is about -5.84 at x = -2.

And the absolute minimum is about -11.28 at x = -π/6.

Step-by-step explanation:

We want to find the absolute maximum and minimum values of the function:

First, we should evaluate the endpoints of the interval:

And:

Recall that extrema of a function occurs at its critical points. The critical points of a function are whenever its derivative is zero or undefined.

So, find the derivative of the function:

Differentiate:

Set the function equal to zero:

And solve for x:

Using the unit circle, our solutions are:

There is only one solution in the interval [-2, 0]:

Thus, we only have one critical point on the interval.

Substituting this back into the function yields:

In conclusion, the absolute maximum value of f on the interval [-2, 0] is about -5.8385 at x = -2 and the absolute minimum value of f is about -11.2782 at x = -π/6.

We can see this from the graph below as well.

b

step-by-step explanation:

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v