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  • Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 28 maths

Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 28 maths

Answers (1)

Answer:

f(x) is increasing for all x.

Given:

f(x)=10^{x}

To find:

We have to show that f(x) is increasing for all x.

Hint:

Condition to be function is increasing i.e, f ‘(x) > 0

Solution:

We have,

f(x)=10^{x}

On differentiating both sides w.r.t. x we get,

\begin{aligned} &f^{\prime}(x)=10^{x} \times \log 10,\left[\therefore \frac{d}{d x} a^{x}=a^{x} \log a\right] \\ &\text { Now, } x \in R \\ &\Rightarrow 10^{x}>0 \\ &\Rightarrow 10^{x} \log 10>0 \\ &\Rightarrow f^{\prime}(x)>0 \end{aligned}

Hence, f(x) is an increasing function for all x.

Posted by

Gurleen Kaur

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