gtamods402
26.11.2019 •
Mathematics
Find the t-coordinates of all critical points of the given function. determine whether each critical point is a relative maximum, minimum, or neither by first applying the second derivative test, and, if the test fails, by some other method.
f(t)= -3t^3+2t
a.) f has (a relative maximum, relative minimum, or no relative extrema) at the critical point t= * (smaller t-value)
b.) f has (a relative maximum, relative minimum, or no relative extrema) at the crtical point t=* (larger t-value)
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Ответ:
f has relative maximum at t =
and
f has relative minimum at t =
Step-by-step explanation:
Data provided in the question:
f(t) = -3t³ + 2t
Now,
To find the points of maxima or minima, differentiating with respect to t and putting it equals to zero
thus,
f'(t) = (3)(-3t²) + 2 = 0
or
-9t² + 2 = 0
or
t² =
or
t =
to check for maxima or minima, again differentiating with respect to t
f''(t) = 2(-9t) + 0 = -18t
substituting the value of t
at t =
f''(t) =
= - 6√2 < 0 i.e maxima
and at t =
f''(t) =
= 6√2 > 0 i.e minima
Hence,
f has relative maximum at t =
and
f has relative minimum at t =
Ответ:
The answer is D.