In each item, do the following analytically: (a) find the

Tyra

Tyra

Answered question

2021-08-17

In each item, do the following analytically: (a) find the relative extrema of f. (b) determine the values of x at which the relative extrema occur. (c) determine the intervals on which f is increasing. (d) determine the intervals on which f is decreasing. f(x)=2(x1)13

Answer & Explanation

unett

unett

Skilled2021-08-18Added 119 answers

(a) Find the domain of the funtion f(x)=2(x1)13, x [1,+) Find the derivative of the function and the domain of the derivetive f(x)=13(x1)23
f(x)=133{(x1)2}, x  {1} Substitute f'(x)=0 ti find the critical points and solve for x 0=13(x1)23
x Since there is no value of x that makes the derivative of the funtion 0, the function has no relative exterma (b) To find x-intercept, substitute f(x)=0 0=2(x1)13 Move expression to th left-hand side and change its sign (x1)13=2 Tranform and simplify the quation (x1)3=2 Raise both sides of the equation to th power of 3 x1=8 Move constant to th right side and change its sign, than calculate x=8+1
x=9 (c) and (d) Let's plot the polynomial to determine the intervals of increasing and decreasing. Decreases by: (,1),(1,) image

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