The function f (x) = the x power of 2 plus the zero of 3x, find its interval,

The function f (x) = the x power of 2 plus the zero of 3x, find its interval,

It is easy to know that f (x) is an increasing function
∵f(-1)= 1/2 -3 0
Therefore, the zero point of F (x) is in the interval (- 1,0)
There is and only one zero point

If the function f (x) = x3-3x + A has three different zeros, the value range of real number a is () A. （-2，2） B. [-2，2] C. （-∞，-1） D. （1，+∞）

Solution ∵ f ′ (x) = 3x2-3 = 3 (x + 1) (x-1),
When x ＜ - 1, f '(x) > 0;
When - 1 < x < 1, f '(x) < 0;
When x > 1, f '(x) > 0,
When x = - 1, f (x) has a maximum value
When x = 1,
F (x) has a minimum, so that f (x) has three different zeros
Just
f(−1)＞0
f(1)＜0 ， The solution is - 2 < a < 2
So choose a

Function f (x) = 3x + 2 to the power of X - the approximate interval where the half zero is located?

3x and 2 ^ x
So the function is incremented
So at most one zero
f(0)=0+1-1/2>0
f(-1)=-3+1/2-1/2<0
Different sign
So x ∈ (- 1,0)
Let's take it together

If the function f (x) = the 3rd power of X - 3x-m has zero on [0,2], the value range of real number m is () The answer is [- 2,2]. After derivation, don't discuss it in three situations. Finally, it is integrated, but the integrated result is inconsistent with the answer. It may be that there is no scope. Thank you! -When m > is equal to 0 and 2-m > is equal to zero, it will be calculated that M is less than or equal to 0

Answer:
F (x) = x ^ 3-3x-m has zero on [0,2]
Derivation:
f'(x)=3x^2-3=3(x^2-1)
00, f (x) is an increasing function
f(0)=-m
f(1)=1-3-m=-2-mf(0)
If f (x) has zero on [0,2], then:
f(2)=2-m>=0,f(1)=-2-m

If the x power of a = 2 and the x power of B = 3, what is the 3x power of (AB)

(ab)^3x=a^3x*b^3x=(a^x)^3*(b^x)^3=2^3*3^3=216

(- 5) to the 3rd power - 3x (- 1 / 2) to the 4th power (- 10) to the 4th power + [(- 4) to the 2nd power - (3 + 3 square) x2]

(- 5) to the 3rd power - 3x (- 1 / 2) to the 4th power
=-125-3 × 1/4
=-125-3/4
=-503/4
(- 10) to the 4th power + [(- 4) to the 2nd power - (3 + 3 square) x2]
=10000+16-12 × two
=10016-24
=9992