Question

A function y=f(x) is said to be minimum at
the point x = a if​

Answer 1

Answer:

What is the options

Step-by-step explanation:

options

Answer 2

Given

• function y=f(x)
• minimum
• point x = a

To find

• the condition for the function to be minimum at a point.

Solution

we are provided with a function and a point X equal to a and are asked to write down the condition for the function to be minimum at the given point.

step 1

we know that a function can only have a absolute minimum or maximum at points where the slope is equal to that of x axis. ie,

at those points, slope of the function should be zero. Therefore there first derivative should be equal to zero.

Mathematically, it can be written as,

f'(a) = 0

step 2

Now we need to predict if the point is a point of maximum or minimum.

This can be predicted by taking the second derivative of the function and substituting the point in the second derivative.ie,

f''(a)

If the value obtained is positive, then we can say that it is a point of minimum or maximum in opposite case.(if negative)

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