Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x)= x³ - 27x+6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function is increasing on (Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed B. The function is never increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function is decreasing on (Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed B. The function is never decreasing. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. Type integers or simplified fractions.) OA. The function has a local minimum f B. The function has a local maximum f OC. The function has a local maximum f( OD. The function has no local extrema. = = = and no local maximum. and a local minimum f() = . and no local minimum.

Q: 4. Use first principles to find the derivative of the function. S(x) = Jx+2

A:

Q: cotcxs-4x)

A: We need to find the derivative of : y=cot(x5-4x)

Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

Q: Let f = e^ (− x ^3/ 3) +x−y^ 2 . Find the local minima, maxima and saddle points.

A:

Q: Sketch the x^2 And the derivative And integration

A:

Q: Use an appropriate local linear approximation to estimate the value (2.03)^3

A:

Q: Find the linearization of the function f(x) = x^(1/5) at a = 32 and use it to approximate…

A: Answer

Q: What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.

A:

Q: Find all values of x where the tangent line is horizontal for the function f (x) = x/x^2+5

A:

Q: find the derivative using implicit differentation

A: Apply derivative on both sides

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: Evaluate the following derivative d/dt (at^2+bt+K)

A:

Q: Let f(x)=11/x^2 + 1 . Enter anti derivative

A:

Q: Explain the three techniques that are used frequently to Use Approximations to Estimate Reversion…

A: Approximations: Approximation is a estimated value or estimation of a number or rounding a number to…

Q: please differentiate the function

A:

Q: _f(x) = = x + 1 ; P(-2, 2)

A:

Q: Explain why the Second Derivative Test is often mistaken for the POI Test. In what way(s) are they…

A: We know the following. POI Test: An inflection point is a point on the graph at which the second…

Q: The approximated value for e using the Maclaurin series expansion coasidering a true relative error…

A: