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Prove that the logarithmic function is s...

Prove that the logarithmic function is strictly increasing on `(0,oo)`.

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To prove that the logarithmic function \( f(x) = \log x \) is strictly increasing on the interval \( (0, \infty) \), we will follow these steps: ### Step 1: Define the function Let \( f(x) = \log x \). ### Step 2: Find the derivative To determine if the function is increasing, we need to find the derivative \( f'(x) \): \[ ...
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.2
  1. Prove that f(theta)=(4sintheta)/(2+costheta)-theta is an increasing fu...

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  2. Find the values of x for which f(x)=[x(x-2)]^2 is an increasing func...

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  3. Show that the function given by f(x) = 3x + 17 is increasing on R.

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  4. Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi...

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  5. Show that the function given by f(x)=e^(2x) is strictly increasing on...

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  6. Find the intervals in which the function f given by f(x)=2x^3-3x^2-36 ...

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  7. Find the intervals in which the function f given by f(x)=2x^2-3xis(a) ...

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  8. Show that y=log(1+x)-(2x)/(2+x),\ x >-1 is an increasing function of x...

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  9. Find the intervals in which the following functions are strictly incre...

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  10. Prove that the function f(x)=x^3-3x^2+3x-100 is increasing on R .

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  11. The interval in which y = x^(2) e^(-x) is increasing is:

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  12. Which of the following functions are decreasing on (0, pi/2)? (a) co...

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  13. On which of the following intervals is the function f given by f(x)=...

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  14. Prove that the logarithmic function is strictly increasing on (0,oo).

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  15. Prove that the function f given by f(x)=x^2-x+1is neither strictly in...

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  16. Prove that the function f given by f(x) = log sin xf(x) = log sin xis ...

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  17. Prove that the function f given by f (x) = log cos xis strictly decrea...

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  18. For what values of a the function f given by f(x) = x^(2) + ax +1 is...

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  19. Let I be an interval disjointed from [-1,\ 1] . Prove that the functio...

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