## Find the intervals in which the function f given by f (x) = 2x² – 3x is (a) strictly increasing (b) strictly decreasing

Question

Find the intervals in which the function f given by f (x) = 2x² – 3x is
(a) strictly increasing (b) strictly decreasing

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2 weeks 2021-10-04T16:29:42+00:00 2 Answers 0 views 0

Given Expression,

We have to find the intervals for which the given function is

• Strictly Increasing
• Strictly Decreasing

Firstly,let us find the derivative of the above function w.r.t. x,

Equating f'(x) = 0 because f'(x) becomes a “constant function” at 0. This would help us find the intervals at which the given function is increasing and decreasing.

• The point (3/4,0) divides the x-axis into two intervals (-∞,3/4) and (3/4,∞).

### Strictly Increasing

• A function is said to be strictly increasing if all values of f'(x) > 0.

Therefore,

f(x) is strictly increasing in the interval (3/4,∞)

### Strictly Decreasing

• A function is said to be strictly decreasing if f'(x) < 0

Therefore,

f(x) is strictly decreasing in the interval (-∞,3/4)

To sum it up,

2. given, f(x) = 2x² – 3x

differentiate f(x) with respect to x,

f'(x) = 4x – 3 ——(1)

(a) when f(x) is strictly increasing function :

f'(x) > 0

from equation (1),

4x – 3 > 0 => x > 3/4

e.g., x ∈ (3/4, ∞ )

Therefore, the given function (f) is strictly increasing in interval x ∈ (3/4, ∞ ) .

(b) when f(x) is strictly decreasing function :

f'(x) < 0

from equation (1),

4x -3 < 0 => x < 3/4

e.g., x ∈ (-∞ , 3/4)

Therefore, the given function (f) is strictly decreasing in interval x ∈ (-∞ , 3/4)

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Step-by-step explanation: