For the given function determine the following: f (x) = (sin x + cos x) 2...

For the given function determine the following: f (x) = (sin x + cos x) 2 ; [−π,π] a) Find the intervals where f(x) is increasing, and decreasing b) Find the intervals where f(x) is concave up, and concave down c) Find the x-coordinate of all inflection points

Expert Solution

milcah answered 2 years ago

f (x) = -0.248226cos (2 x) - 0.0184829cos ((2+2)x) - 0.0594608cos(x)sin(x) + 0.123626*sin ((2+2)x). The intervall...

f (x) = -0.248226*cos (2 x) - 0.0184829*cos ((2+2)x) - 0.0594608*cos(x)*sin(x) + 0.123626*sin ((2+2)x). The intervall is ]0, 3/2[ What is the local maximum and local minimum? Answer with 5 decimals

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) = ...

S(x) is a cubic spline for the function f(x) = sin(pi x/2) + cos(pi x/2) at...

S(x) is a cubic spline for the function f(x) = sin(pi x/2) + cos(pi x/2) at the nodes x0 = 0 , x1 = 1 , x2 = 2 and satisfies the clamped boundary conditions. Determine the coefficient of x3 in S(x) on [0,1] ans. pi/2 -3/2

Consider the function given as example in lecture: f(x, y) = (e x cos(y), ex sin(y))...

Consider the function given as example in lecture: f(x, y) = (e x cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f −1 be a continuous inverse of f defined in a neighborhood of b. Find an explicit formula for f −1 and compute Df−1 (b). Compare this with the derivative formula given by the Inverse Function Theorem.

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = tan(x) + 2

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = tan(x) + 2

Find the absolute maximum and absolute minimum values of f(x) = cos(2x)+2 sin(x) in the interval...

Find the absolute maximum and absolute minimum values of f(x) = cos(2x)+2 sin(x) in the interval [0; pi]

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = log2 (x)

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = log2 (x)

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2...

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2 = 0.5. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.15)

Consider the function f(x) = x 4 − 4x 2 . Determine the following: • The...

Consider the function f(x) = x 4 − 4x 2 . Determine the following: • The (x,y) coordinate pairs of the local minima and local maxima. • The (x,y) coordinate pair of the absolute minimum and absolute maximum, should they exist. If the absolute min/max is obtained at multiple points, list all of them. • The intervals of increasing and decreasing. • The intervals of concavity. That is, explain exactly where this function is convex and exactly where this function...

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