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Prove that f(x)=a^x, 0<a<1, is decreasin...

Prove that f(x)=`a^x`, `0`<`a`<`1`, is decreasing in R.`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The function defined by f(x)=(x+2)e^(-x) is decreasing for all x decr...

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  2. Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even ...

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  3. Prove that f(x)=a^x, 0<a<1, is decreasing in R.

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  4. Assertion Consider the following statements in S and R S: Both sinx a...

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  5. Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Stat...

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  6. Statement 1: f(x)=|x-1|+|x-2|+|x-3| has point of minima at x=3. State...

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  7. Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...

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  8. Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x...

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  9. Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima...

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  10. If a function f(x) has f^(prime)(a)=0 and f^(primeprime)(a)=0, then (...

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  11. The minimum value of 2^((x^2-3)^3+27) is (a) 2^(27) (b) 2 (c) 1 (d...

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  12. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q ...

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  13. The maximum value of ((logx)/x)is

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  14. The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N, has a local minimum...

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  15. Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...

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  16. The equation e^(x-1)+x-2=0 as

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  17. The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the i...

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  18. If [.] denotes the greatest integer function then lim(x→0)​[x^2/(tanx....

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  19. If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...

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  20. The real number x when added to its inverse given the minimum value of...

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