y'= 1/(x+a)

Let the tangent point be P(s, t),

P is on the tangent y=x+ 1 :t=s+ 1 ( 1)

P on the curve y=ln(x+a): t=ln(s+a)? (2)

Tangent slope = tangent point derivative: 1/(s+a)= 1 (3)

(3)== >s+a= 1？ Substitution? (2) Yes

? t=0？ Substitution? ( 1)? Have to? s=- 1

∴? a=2？

2. What is the tangent equation of curve y=x/(x-2) at point (-1, 1)?

y'=-2/(x-2)？

∴ Tangent slope k=y'|(x=- 1)=-2/9

The tangent equation is: y- 1=-2/9(x+ 1)

Namely. 2x+9y-7=0

3. There are two points A (4,0) and B (2,4) on the curve Y = 4x-x 2. If the tangent of point P on the curve is exactly parallel to the chord AB, what is the coordinate of point P?

Y'=4-2x, and set the tangent point P(x0, y0).

AB slope kAB=(4-0)/(2-4)=-2.

According to the meaning of the question: y'|(x=x0)=4-2x0=-2.

∴x0=3,y0=4x0-x0^2=3

∴P(3,3)

4. What is the monotonic increasing interval of the function f (x) = (x-3) e x?

f'(x)=e^x+(x-3)e^x=(x-2)e^x

By who? F'(x)>0 is x-2 >: 0? Have to? x & gt2

The monotone increasing interval of ∴ is (2, +∞)

5. If the function f (x) = x 3+ax has two extreme points on R, what is the range of the real number A?

f'(x)=3x^2+a

∵f(x) has two extreme points on r.

∴f'(x) has two different zeros.

∴a<； 0

6. What are the maximum and minimum values of the function f (x) = x 3-3x+ 1 in the closed interval?

f'(x)=3x^2-3=3(x+ 1)(x- 1)

F'(x)=0？ X=- 1 or x= 1? (1 is not in the interval, so it is not considered)

List:

f(x)max=f(- 1)=3？ ，f(x)min=f(-)=- 17？