Consider the following function on the given interval. f(x)=17+2x-x^{2}, \ \

Dowqueuestbew1j

Dowqueuestbew1j

Answered question

2021-12-08

Consider the following function on the given interval.
f(x)=17+2xx2,   [0,5]
Find the derivative of the function.
f'(x)=
Find any critical numbers of the function.
x=
Find the absolute maximum and absolute minimum values of f on the given interval.

Answer & Explanation

Donald Cheek

Donald Cheek

Beginner2021-12-09Added 41 answers

Step 1
Given
f(x)=17+2xx2 and the interval [0, 5]
differentiating with respect to x,
f'(x)=2−2x
Step 2
To find critical numbers we put
f'(x)=0
22x=0
2x=2
x=1
Hence, the only critical number of the function is x=1.
Step 3
To find the absolute minimum value and the absolute maximum value of the function, we check the function value at critical point and at the boundary points.
We have
f(x)=17+2xx2
f(1)=17+2-1=18
f(0)=17+0-0=17
f(5)=17+10-25=2
Hence,
absolute minimum value = 2
absolute maximum value = 18

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