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Find the intervals in which the function f given by f(x) = 2x^

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Find the intervals in which the function $f$ given by $f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7$ is (a) strictly increasing (b) strictly decreasing.

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Find the intervals in which the function

f

given by

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7

is (a) strictly increasing (b) strictly decreasing.

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

The given function is

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7

f^{'} (x) = 6 x^{2} - 6 x - 36 = 6 (x^{2} - x - 6) = 6 (x + 2) (x - 3)

∴ f^{'} (x) = 0 \Rightarrow x = - 2, 3

The points

x = 2

and

x = 3

divide the real line into three disjoint intervals

i.e.,

(- \infty, - 2), (- 2, 3),

and

(3, \infty) .

In intervals

(- \infty, - 2)

and

(3, \infty), f^{'} (x) > 0

while in interval

(- 2, 3), f^{'} (x) < 0

Hence, the given function

(f)

is strictly increasing in intervals

(- \infty, - 2)

and

(3, \infty)

while function (f) is strictly decreasing in interval

(- 2, 3) .

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Question Text	Find the intervals in which the function $f$ given by $f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7$ is (a) strictly increasing (b) strictly decreasing.
Answer Type	Text solution:1
Upvotes	150

Find the intervals in which the function f given by f(x)=2x3−3x2−36x+7 is (a) strictly increasing (b) strictly decreasing.

Text solutionVerified

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Find the intervals in which the function $f$ given by $f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7$ is (a) strictly increasing (b) strictly decreasing.