Find any open intervals on which the given function is increasing. Find any open intervals on which the given function is decreasing. (a) f(x) = (x – 2)(x + 3)2 (b) g(x) = (x – 4) Vx, x > 0 (c) h(x) = sin(x) + cos(x), 0 < x < 2m
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- In the function: f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and minima in the function?Find the absolute maximum and absolute minimum of the function f ( x ) = x 2 e -x on the closed interval [ 1 , 4 ].Find the absolute minimum and absolute maximum of f(x)=ln(x2+10x+16) over the interval [0,4]
- Find the absolute minimum and absolute maximum of f(x) = ln(x2+10x+16) over the interval [0,4]A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.Find all the critical points and local maximums and minimums of each function. f(x) = 5x+cos(2x+1)
- The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270.f(x) has one local minimum and one local maximum.f(x) has a local minimum at x equals_______, with value ________ and a local maximum at x equals _____ with value ________Find the local and absolute maximum and minimum values of f(x) f(x) = cos x, x ∈ [-3pi/2 , 3pi/2 ].Find the value of x for which the function f(x) = 3x^4 - 8x^3 + 6x^2 + 2x + 1 has a critical point.
- Find the maximum and minimum values of the function f(x) = ln(x)/x on the interval [1, 3]In the function: f(x)=(12−3x)e^x What are the critical numbers of the function? When is the function increasing and decreasing in interval notation? What are the x-coordinates of all local minimums and maximums?The function ff has a continuous second derivative, and it satisfies f(1)=2f(1)=2, f′(1)=0f′(1)=0 and f′′(1)=2f″(1)=2. We can conclude thatA. ff has a local maximum at 1B. ff has a local minimum at 1C. ff has neither a local maximum nor a local minimum at 1D. We cannot determine if A, B, or C hold without more information.