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Second Derivative Test Choose the most appropriate answer for each question. Drag the correct answer into each blank. fundamental theorem $y = -x^4$ $f''(d) = 0$ critical point theory does local minimum neither $f''(c) > 0$ $f''(d) < 0$ $f'(x)$ is undefined $f''(d) > 0$ second derivative test $f'(b) = 0$ $f''(b) < 0$ first derivative test $f'(d) = 0$ $f'(a)$ is undefined $f''(b) > 0$ $f'(c) = 0$ $y = x^4$ local maximum $f''(c) = 0$ does not $f''(c) < 0$ $y = x^3$ $f''(b) = 0$ For these problems, we don't know the formula for the function $f(x)$. #1. For the graph $y = f(x)$, the second derivative test guarantees that (i) The point $(c, f(c))$ is a local minimum provided that: $f'(a) = 0$ and

          Second Derivative Test
Choose the most appropriate answer for each question. Drag the correct answer into each blank.
fundamental theorem  $y = -x^4$  $f''(d) = 0$ critical point theory does
local minimum neither $f''(c) > 0$ $f''(d) < 0$ $f'(x)$ is undefined $f''(d) > 0$
second derivative test $f'(b) = 0$ $f''(b) < 0$ first derivative test $f'(d) = 0$
$f'(a)$ is undefined $f''(b) > 0$ $f'(c) = 0$ $y = x^4$ local maximum $f''(c) = 0$ does not
$f''(c) < 0$ $y = x^3$ $f''(b) = 0$
For these problems, we don't know the formula for the function $f(x)$.
#1. For the graph $y = f(x)$, the second derivative test guarantees that
(i) The point $(c, f(c))$ is a local minimum provided that:
$f'(a) = 0$ and

Show more…

Second Derivative Test
Choose the most appropriate answer for each question. Drag the correct answer into each blank.
fundamental theorem y = -x^4 f”(d) = 0 critical point theory does
local minimum neither f”(c) > 0 f”(d) < 0 f'(x) is undefined f”(d) > 0
second derivative test f'(b) = 0 f”(b) < 0 first derivative test f'(d) = 0
f'(a) is undefined f”(b) > 0 f'(c) = 0 y = x^4 local maximum f”(c) = 0 does not
f”(c) < 0 y = x^3 f”(b) = 0
For these problems, we don't know the formula for the function f(x).
#1. For the graph y = f(x), the second derivative test guarantees that
(i) The point (c, f(c)) is a local minimum provided that:
f'(a) = 0 and

Added by Juana H.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Madhur L

05/19/2023

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Transcript

00:01 Hi, now we have to find the x coordinates of the critical points and determine if each relative maxima or minima or neither.

00:09 So now fx is given to us as 2x to the power 6 minus 3x to the power 4.

00:14 So for critical points we put f dash derivative x equal to 0.

00:18 So f derivative x will be equal to 12x to the power 5 minus 12x cube and we put equal to 0.

00:24 So this is 12x cube into x square minus 1 is equal to 0.

00:29 So from here we have either x is equal to 0 or x is equal to plus 1 or x is equal to minus 1.

00:35 So now we have the 3 critical points.

00:38 So we find f double derivative x.

00:40 So f double derivative x will be equal to 60x to the power 4 minus 36x square.

00:46 So f double derivative 0 is 0.

00:48 So double derivative test fails over here.

00:52 We will use single derivative test, first derivative test for this now.

00:56 F double derivative at minus 1 will be 60 minus 36 which is greater than 0.

01:02 So therefore this is the point of local minimum.

01:10 Now f double derivative at 1 is 60 minus 36 which is again greater than 0.

01:16 So again x is equal to 1 is the point of local minimum.

01:21 Now we have to check for 0...

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