Find the points of local maxima or local minima, if any, of the functi

1.	Find the points of local maxima or local minima, if any, of the 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
Answer» Given as f(x) = (x – 5)⁴ On differentiating with respect to x f’(x) = 4(x – 5)³ For the local maxima and minima f‘(x) = 0 = 4(x – 5)³ = 0 = x – 5 = 0 x = 5 f‘(x) the changes from negative to positive as passes through 5. Therefore, x = 5 is the point of local minima Hence, local minima value is f (5) = 0

Find the points of local maxima or local minima, if any, of the 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

Answer»

Given as f(x) = (x – 5)⁴

On differentiating with respect to x

f’(x) = 4(x – 5)³

For the local maxima and minima

f‘(x) = 0

= 4(x – 5)³ = 0

= x – 5 = 0

x = 5

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

Therefore, x = 5 is the point of local minima

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