Question

A Content attribution QUESTION 12.1 POINT Use the First Derivative Test to find the location of all local extrema for the function given below. Enter an exact answer. If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter in the appropriate box. 202 f(x) = -x + +1 Provide your answer below: • Local maxima occur at x = • Local minima occur at x = FEEDBACK Content attribution MacBook Air

Answer 1

First, we have to find the critical points of the function f(x) by equating f'(x)=0 and solve for x.

Then, by checking the sign change of f'(x) while moving from left to right of the critical point, we have found out the location of local extrema. The step by step explanatory solution is provided below.

Use the Question 12 derivative Test to find the location of all local extrema for the function given below, fra)= x+201²+1 +1 Solution 12. Step) To 50 da 3 Step 2 To check the let Fru)=– alt 2013 find all the critical points of frus, we put pix)= d (-x9+ 20x3 +) - 4 +20 (342) +0=o » –4x3+ 2032-0 » (-x+5) = 0 =n=0, locel Maximum prinimum at prinimum at são. Evaluate F(-) = – 4(4)3 + 20 (4)2 – – 4(+) +20 = f'(I) = -40113 + 20112 = while moving from Left to right of This By finet derivative Test, there is neither local linimum at nad 124 yo 70 16 - 4+ 20 = since, there is in the signo change ho 0 Maximum hor Now, to check at n=5. 16470 Fly4co Evadereting flou) = -4643 + 2004.-256+ 320 = F'(6) = 4(6)3 + 20 (6) ²2 – 864+ 720 = Therefore, by finet derivative Test, free) has local Maximum at [n=5