Differentiation : Find Local Extrema of a Function on an Interval

Locate the absolute extrema of the function on the closed interval. f(x) = -x^2 + 3x [0,3] [Answer is minimum at (0,0) and (3,0) and max at (3/2), 9/4)

Locate the absolute extrema of the function on the closed interval. g(t) = t^2/t^+ 3 [-1,1] Answer Min (0,0) Max (-1, 1/4) (1, 1/4)

Locate the absolute extrema of the function on the closed interval. y = e^x sin x [0,pi] Answer: Min: (0,0) (pi,0) Max (3pi/4, square root of 2/2(e^3pi/4)

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Differentiation
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Locate the absolute extrema of the function on the closed interval. f(x) = -x^2 + 3x [0,3] [Answer is minimum at (0,0) amd (3,0) ...

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Local extrema are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

...Find the extrema of f on the given interval. ... For extreme values, we equate the derivative to zero. This gives . ... The function has local minimum at . ...

... which implies that at that point attains a local extrema. ... 1.15) The other is (1.16) To find the type of ... (1.17) At we have: (1.18) The derivative is definitely ...

... Sketch the graph of y = f(x), and identify any local maxima and minima. ... to find the intervals, find the derivative, and the critical points. ...

... f(1) = 3 when when Let Find the following. ...Local Extrema and Volume of a Solid of Revolution are ... The graph of the derivative of a function f ...

... 2. Given that f is a differentiable function and the graph of its derivative is shown below, find... 3. Find the critical numbers and the local extreme values ...

... 2. If the first derivative f' is negative (-) , then the ... Problem: Find the interval on which the function 2 2 ... of y = f(x), and identify any local maxima and ...