Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x)=x2−6x−8; [0,5]

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Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.  f(x)=x2−6x−8; [0,5]

levurdondishav4 · Accepted Answer

Step 1Given function is f(x)=x2−6x−8To find the absolute minimum values over the interval [0, 5], we need to find the critical points and substitutecritical points and boundary points and find the values of x at which maximum and minimum of function occurs.To find critical points, evaluate f&#039;(x) = 0Step 2f(x)=x2−6x−8f′(x)=ddx(x2−6x−8)=2x-6f&#039;(x)=0⇒2x−6=02x=6x=62x=3Step 3substitute x = 0, x=3, x=5 in f(x)at x=0f(0)=02−(6×0)−8=-8at x=3f(3)=32−(6×3)−8=-17at x=5f(5)=52−(6×5)−8=-13Absolute maximum value of f(x) is -8 at x = 0Absolute minimum value of f(x) is -17 at x = 3

Find the absolute maximum and minimum values of the function

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