If the function f (x) = ax ^ 2 + 2x + blnx, take the extremum when x = 1 and x = 2. (1) find a, B (2) find the monotone interval of the function

(1) F '(x) = 2aX + 2 + B / X. f' (1) = 2A + 2 + B = 0, f '(2) = 4A + 2 + B / 2 = 0. The solution is a = - 1 / 3, B = - 4 / 3. (2) f (x) = - (1 / 3) x ^ 2 + 2X-4 / (3lnx), f' (x) = - (2 / 3) x + 2-4 / (3x) = - 2 (x ^ 2-3x + 2) / (3x) = - 2 (x-1) (X-2) / (3x). The monotone increasing interval of F (x) is (1,2), and the decreasing interval is (0,1

Given the function f (x) = ax + blnx, the tangent equation of this function at (1, f (1)) is y = 1. Find the monotone interval and extremum of F (x)

The tangent at x = 1 is y = 1, which means the slope is 0
That is, a + B = 0, a = - B
So f '(x) = - B + B / x = B (1 / x-1)
The domain is (0, + ∞)
When B = 0, f (x) is equal to 0, it is meaningless to discuss monotone interval and extremum
b> 0:00
When x = 1, there is a maximum - B, 0

If the function f (x) = ax ^ 2 + 2x + blnx, take the extremum when x = 1 and x = 2
(1) Find a, B
(2) Finding the maximum and minimum on [1 / 2,2]
My friend, I can do the first question. I prefer the process + answer of the second question

f'(x)=2ax+2+b/x
f'(1)=2a+2+b=0
f'(2)=4a+2+b/2=0
a=-1/3
b=-4/3
F '(x) = (- 2 / 3) x-4 / 3x + 2 according to the image, f (1) is the minimum and f (2) is the maximum
By comparing f (1 / 2) with F (2), f (1 / 2) is the maximum

1. The parabola y = ax & # 178; + BX + C passes through the point a (- 1,2) and the straight line y = X-1 and the two intersections B and C of the x-axis and y-axis
2. The symmetry axis of a quadratic function is a straight line x = 2, the maximum value is - 3, and its image passes through (0,11)
Be specific

(1) Y = ax & # 178; + BX + C passes through point a (- 1,2) and the intersection points B (1,0) and C (0, - 1) of the line y = X-1 and X axis and Y axis, substituting a, B, C into y = ax & # 178; + BX + C, a = 2, B = - 1, C = - 1, y = 2x & # 178; - X-1 (2) the symmetry axis of a quadratic function is a straight line, x = 2, the minimum value is - 3, and its image passes through (0,11)

What's the difference between solving problems by equation and by arithmetic?

Using equation solution is to take the number of required solutions as a known number, list the management according to the meaning of the problem, and then calculate the unknown quantity according to the change of the identity. Using formula solution is to use the known number to list the formula for directly calculating the unknown quantity through a certain physical meaning. The equation is simpler. If you have to use formula solution, you can also borrow

Why do the two methods of measuring resistance by voltammetry not strictly meet Ohm's law

Because the voltmeter and ammeter are not ideal
The ammeter has internal resistance, which brings new resistance value to the circuit
Voltmeter resistance is not infinite, can not be regarded as open circuit
These two methods do not strictly satisfy Ohm's law, they can not strictly verify Ohm's law, because there are errors

Help me solve some factoring problems
ab^2-2a^2b+a^3 2x^2-12x+18 19.5^2-0.5^2 56^2+44^2+56*88

ab^2-2a^2b+a^3=a(a-b)^2
2x^2-12x+18=2(x-3)^2
19.5^2-0.5^2=(19.5-0.5)*(19.5+0.5)=380
56^2+44^2+56*88=(56+44)^2=10000

Uncle Li deposits 2000 yuan in the bank for two years. He gets 171 yuan after tax interest when he matures. What's the annual interest rate? (5% interest tax)

Suppose the interest is X
2000*X*2*(1-5%)=171
The solution of the equation is x = 0.045
That is, x = 4.5%, and the interest rate is 4.5%

In △ ABC, ab = AC, the vertical bisector of AB intersects AC at D, and the perimeter of △ ABC and △ DBC are 60cm and 38cm respectively
Because the vertical bisector of AB intersects AC at D
So ad = BD
Because AB + AC + BC = 60, BD + BC + CD = 38
So AD + BC + CD = 38, that is, AC + BC = 38,
So AB = 60-38 = 22,
So BC = 60-22-22 = 16
So the length of each side of △ ABC is 22cm, 22cm and 16cm respectively
How do you get AC + BC = 38 here?

AD+CD=AC
The common endpoint is d

Today is Tuesday. What day is tomorrow?

Well, Wednesday

If the function f (x) = ax ^ 2 + 2x + blnx, take the extremum when x = 1 and x = 2. (1) find a, B (2) find the monotone interval of the function