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General

Easy

Question

# The interval of increase of the function is

Hint:

### We are given a function. We have to find the interval for which it is increasing. We will take the first order derivative to find the answer

## The correct answer is:

### The given function is

A function is said to be increasing when it’s first order derivative is positive.

It means f’(x) > 0

We will use this condition to find the answer.

Taking the first order derivative of the given function.

f(x) =

f’(x) = 1 – e^{x} + 0

Now for the function to be increasing,

f'(x) > 0

1 - e^{x} > 0

1 > e^{x}

e^{x }< 1

Taking log_{e} of both the sides. It means we are taking natural log on both the sides.

xlog_{e}e < log_{e}1

x < 0 ...{ log_{e}e = 1 and log_{e}1 = 0}

x can have any value less than zero.

There is no lower limit on x.

So, the interval will be (-∞,0)

For such questions, we should know different formulas of differentiation.

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