Find the points of local maxima or local minima, functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be f (x) = (x – 5)4

Asked by Sakshi | 1 year ago |  72

##### Solution :-

Given f (x) = (x – 5)4

Differentiate with respect to x

f’(x) = 4(x – 5)3

For local maxima and minima

f‘(x) = 0

= 4(x – 5)3 = 0

= x – 5 = 0

x = 5

f‘(x) changes from negative to positive as passes through 5.

So, x = 5 is the point of local minima

Thus, local minima value is f (5) = 0

Answered by Aaryan | 1 year ago

### Related Questions

#### Given the sum of the perimeters of a square and a circle, show that the sum of their areas is least when one side

Given the sum of the perimeters of a square and a circle, show that the sum of their areas is least when one side of the square is equal to diameter of the circle.

#### A wire of length 20 m is to be cut into two pieces. One of the pieces will be bent into shape

A wire of length 20 m is to be cut into two pieces. One of the pieces will be bent into shape of a square and the other into shape of an equilateral triangle. Where the wire should be cut so that the sum of the areas of the square and triangle is minimum?

#### A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?