1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θ

1) Find the critical numbers of the function.

f(θ) = 16 cos θ + 8 sin^2 θ

θ=?

2) Find the absolute maximum and absolute minimum values of f on the given interval.

f(x) = x/(x^2 − x + 9), [0, 9]

3) f(x) = 3x³ + 4x² + 7x + 5, a = 5

(f ⁻¹)'(a) = ?

Expert Solution

milcah answered 2 years ago

(tan2(θ) − 16)(2 cos(θ) + 1) = 0

Solve the given equation. (tan2(θ) − 16)(2 cos(θ) + 1) = 0 θ =

Express sin 6θ as a polynomial in sin θ and cos θ.

If 3/(2+ cos θ+i sin θ) = a+ib, then [(a-2)2+b2] is

3. Let g(θ) = 2 cos(θ) + sin(2θ) . Find the absolute maximum and minimum values...

3. Let g(θ) = 2 cos(θ) + sin(2θ) . Find the absolute maximum and minimum values of g on the interval [0, π/2]

Given H = (3R^2/ sin θ) aθ + 54 R cos θ aφ A/m (a) Find...

Given H = (3R^2/ sin θ) aθ + 54 R cos θ aφ A/m (a) Find J. (b) Find the total current in the aθ direction through the conical surface θ = 20◦, 0 ≤ φ ≤ 2π, 0 ≤ R ≤ 5 Please explain (b) thoroughly.

1. For the following function ?(?) = (?^2−8?+16) / (?^2−4) a. Find the critical values b....

1. For the following function ?(?) = (?^2−8?+16) / (?^2−4) a. Find the critical values b. Use the FIRST DERIVATIVE TEST to determine the intervals where the function is INCREASING and DECREASING. c. Find the RELATIVE EXTREMA of the function and state where they occur. d. Find the ABSOLUTE EXTREMA of the function on the interval [−1, 1.75]

Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))^2 (a) Find...

Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))^2 (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify the relative extrema. relative maximum (x, y) = relative minimum (x, y) =

Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find...

Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing ( ) decreasing ( ) (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (x, y) = ( ) (larger x-value) relative minima (x, y) = (smaller x-value) (x, y) = ...

Find the values of sin θ, cos θ, and tan θ for the given right triangle. Give the exact values.

Exercise 4: Find all local extrema for f ? = sin^2 ? + cos ? on...

Exercise 4: Find all local extrema for f ? = sin^2 ? + cos ? on the interval [− ?/ 2 , ?/ 2 ]. Verify your answer by graphing.

Question