Find Points Of Local Maximum And Local Minimum Of

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Question

Find points of local maximum and local minimum of

easy

Solution

Correct option is

x = 0

Differentiate f (x) w.r.t x to get:

The only critical point is x = 0.

Let us observe the sign change of f’(x) at critical point x = 0.

Use the following figure to check how sign of f’(x) is changing about x = 0.

x = 0 is the only point of local minimum as f’(x) changes sign from negative to positive values.

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SIMILAR QUESTIONS

Q1

Find the point of local maximum and local minimum of

easy View solution

Q2

Find points of local maximum and local minimum of f(x) = x² e^–x.

easy View solution

Q3

Find points of local maximum and local minimum of f (x) = x^2/3 (2x – 1).

medium View solution

Q4

Identify the absolute extrema for the following function.

f (x) = x² on [–1, 2]

easy View solution

Q5

Identify the absolute extrema for the following function.

f (x) = x³ or [–2, 2]

easy View solution

Q6

Determine the absolute extrema for the following function and interval.

g(t) = 2t³ + 3t² – 12t + 4 on [– 4, 2]

easy View solution

Q7

Find the local maximum and local minimum values of the function y = x^x.

easy View solution

Q8

A window is in the form of a rectangle surmounted by a semi-circle. The total area of window is fixed. What should be the ratio of the areas of the semi-circular part and the rectangular part so that the total perimeter is minimum?

diffcult View solution

Q9

A box of constant volume C is to be twice as long as it is wide. The cost per unit area of the material on the top and four sides is three times the cost for bottom. What are the most economical dimensions of the box?

diffcult View solution