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

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To show that the function \( f(x) = 3x + 17 \) is strictly increasing on \( \mathbb{R} \), we will follow these steps: ### Step 1: Find the First Derivative To determine whether the function is increasing or decreasing, we first need to find the first derivative of the function \( f(x) \). \[ f'(x) = \frac{d}{dx}(3x + 17) \] ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6.2
  1. Show that the function given by f (x) = 3x + 17is strictly increasing...

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

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

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

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

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

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

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

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  9. Prove that y=(4sintheta)/((2+costheta))-theta is an increasing func...

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

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  11. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

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  12. Which of the following functions are strictly decreasing on [0,pi/2](...

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  13. On which of the following intervals is the function x^(100)+sinx-1 dec...

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  14. Find the least value of a such that the function f given by f(x)=x^2+...

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  15. Let I be any interval disjoint from (1, 1). Prove that the function f...

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  16. Prove that the function f given by f(x) = log sin x" is increasing on...

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  17. Prove that the function f given by f(x) = log | cos x|" is decreasing ...

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

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  19. The interval in which y=x^2""e^(-x) is increasing is (A) (-oo,""""o...

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