How to judge the zeros of a function For example, f (a) f (b)

How to judge the zeros of a function For example, f (a) f (b)

The most intuitive way to judge the zero point of a function is drawing
For example: | x | = 1 + ax has a negative root and no positive root, find the value range of A
|X | = 1 + ax is equivalent to x ^ 2 = (1 + ax) ^ 2, and (a ^ 2-1) x ^ 2 + 2aX + 1 = 0 has a negative root and no positive root. Then a ^ 2-1 is discussed
When a ^ 2-1 = 0, i.e. a = 1, - 1, it can be obtained that a = 1 holds and a = - 1 does not
When a ^ 2-10, the combined image delta > = 0 - B / 2A1
Then the three cases are combined to get a > = 1
f(a)f(b)

The derivative of the function y = log2x at x = 4 is

y=log2x=lnx/ln2
y'=1/(xln2)
x=4,y'=1/(4ln2)

Why is the second derivative of a function greater than 0 and its original function concave?

The first derivative of a function reflects the monotonicity of the function. The second derivative is the derivation of the first derivative. If the second derivative is greater than 0, it means that if the first derivative increases, the absolute value of the tangent slope of the original function decreases continuously in the process of the first derivative increasing from negative infinity to zero. When the first derivative is zero, the tangent level of the original function increases. When the first derivative increases from zero to positive infinity, the tangent slope of the original function decreases continuously, The tangent slope of the original function increases continuously, so the whole function shows a trend of decreasing first and then increasing

The function f (x) = the power of X + the power of a / X (a is greater than 0, the derivative of a is 0, then x?

f′=2x-a^2/x^2=0,
2x^3-a^2=0,
x=1/2·(3)√(4a^2)

Function f (x) = {x (1-x) ^ 1 / x, x = 0; left derivative f 'at x = 0_ (0) yes____

Function
　　f(x) = x(1-x)^(1/x),x=0,
The left derivative at x = 0 is
　　f'-(0) = lim(x→0-)[f(x)-f(0)]/x
　　= lim(x→0-){[x(1-x)^(1/x)]-0}/x
　　= lim(x→0-)[(1-x)^(1/x)]
　　= e^(-1).

The third problem is to find the sum function of power series,
 

As shown in the picture

Finding the sum function of power series X ^ (n-1) / (N2 ^ n)

Find the sum function of the power series [∞Σ n = 1] [(2n-1) * x ^ (2n-2)] and find [∞Σ n = 1] (2n-1) / 2 ^ (n-1)
The sum function has been calculated to be (1 + x ^ 2) / (1-x ^ 2) ^ 2. The sum answer is 6

What function is defined as R, but can only be derived at one point

The function R (x) is defined as follows:
When x is a rational number, R (x) = x & # 178;,
When x is irrational, R (x) = 0,
This function satisfies your requirements
I don't need to prove that the derivative at x is 0. At x ≠ 0, the function is discontinuous, so it is not differentiable

It is proved that a function is differentiable and continuous in its domain. An example is the best

For example:
y=x^2
It is continuously differentiable over the domain R;
y'=2x .