Please prove the monotonicity of exponential function Proof Halo, what is derivative? Is there another way?
The exponential function f (x) = a ^ x, a > 0, and a! = 1. (Note: the requirement of the exponential function for the base number, otherwise it is not an exponential function,! = is not equal to the sign). The derivation of F '(x) = a ^ x ln a, because a ^ x > 0 is always true, so there are: when 0 < a < 1, ln a < 0, f' (x) < 0, the
If f (x) = (A-3) (A-2) x is an exponential function, find the value of F (3)
Is f (x) = (A-3) (A-2) x an exponential function?
Given that the function f (x) = loga1 mxx + 1 (A & gt; 0, a ≠ 1, m ≠ - 1), is an odd function defined on (- 1,1). (I) find the value of F (0) and the value of real number m; (II) judge the monotonicity of function f (x) on (- 1,1) when m = 1, and give the proof; (III) if f (12) & gt; 0 and f (b-2) + F (2b-2) & gt; 0, find the value range of real number B
(1) ∵ f (0) = loga1 = 0. Because f (x) is an odd function, f (- x) = - f (x) {f (- x) + F (x) = 0 ∵ log a & nbsp; MX + 1-x + 1 + log a 1-mxx + 1 = 0; ∵ log a & nbsp; MX + 1-x + 1 · 1-mxx + 1 = 0 {MX + 1-x + 1 · 1-mxx + 1 = 1, that is ∵ 1-mx2 = 1-x 2 for X in the domain