Using FPI, find a critical point of the function: f(x) = x2 – 2e* cos x With an initial guess, xo 0.5
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- Find the local and absolute maximum and minimum values of f(x) f(x) = cos x, x ∈ [-3pi/2 , 3pi/2 ].Find the critical numbers of the function. h(x) = sin2 x + cos x, 0 < x < 2Use the closed interval method to find the absolute maximum and absolute minimum of f(x)= 2 cos x+ sin 2x of the interval [0,π/2]
- Find the critical numbers of the function. If an answer does not exist, put DNE.Find the minimum and maximum values of the function on the given interval by comparing values at the critical points and endpoints. y=cos θ + sin θ , [0, 2π]Find all critical points of the function: R(θ) = cos θ + sin2 θ
- Find the critical numbers of the function f(x) = 2cos x + sin 2 xFind the critical numbers of f(x) = x4(x-1)3 A. What does the second derivative test tell you about the behavior of f at these critical numbers? B. What does the first derivative test tell you?Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π. Find all critical points of f(x) (exact value)
- Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)).c = Use the Second Derivative Test to determine whether it is• A. a local maximum• B. a saddle point• C. a local minimum• D. test failsFind all values of x in the interval [ -pi/2, pi/2 ]at which the fuction f(x)=sin^2+cos x reaches an absolute minimum value. Note: The only x values in this interval where f'(x)=0 are x= - pi/3 and x= pi/3Find the critical value(s) of f(x) = x + 2sin (x) on the interval 0<=x<=2pi b) Classify each critical value as a minimum, maximum, or stationary point. (Explainyour answer)