If the line y = 2x + 1 is a tangent of the curve y = x ^ 3-x-a, find the value of the real number a

y'=3x^2-1=2
X = ± 1, y = 3 or - 1
Substitute y = x ^ 3-x-a to get
a=-3,a=1

RELATED INFORMATIONS

1. If f (x) = x ^ 3-3x ^ 2-3mx + 4 has a maximum value of 5, find the value of the real number m and the tangent equation of the curve y = f (x) passing through the origin
2. If the line y = KX + 4 intersects the circle x ^ 2 + y ^ 2 = 1 or the curve y ^ 2 = x, then the value range of K is?
3. Given that hyperbola y = 3x and straight line y = KX + 2 intersect point a (x1, Y1) and point B (X2, Y2), and X12 + X22 = 10, find the value of K
4. The maximum range of objective function z = 3x + 2Y is [7,9], then the range of positive real number k is
5. Let the real numbers x and y satisfy the following conditions: ① x-y-2 ≤ 0, ② x + 2y-4 ≥ 0, ③ 2y-3 ≤ 0, then the maximum value of Y / X is Note: I hope you can give me a picture!
6. If the lines X + 2y-1 = 0 and y = KX are parallel to each other, then the value of the real number k is______ ．
7. K stands for real number. The curve represented by equation kx2 + 2y2-8 = 0 is discussed
8. For any real number k, what is the position relationship between the line (3K + 2) x-ky-2 = 0 and the circle x ^ 2 + y ^ 2-2x-2y-2 = 0? The relationship between the center of a circle and a straight line is discussed without over fixed point method
9. For any real number k, if the line (3K + 2) x-ky-2 = 0 passes a certain point, then the fixed point
10. The line L: kx-y-4k + 3 = 0 K belongs to the positional relationship between R and x ^ 2 + y ^ 2-6x-8y + 12 = 0
11. Find a tangent of the curve y = X3 + 3x2-5, so that the tangent is perpendicular to the straight line 2x-6y + 1 = 0 - (X3 is the third power of X, 3x2 is three times the square of x)
12. RT tomorrow midterm exam this question is the original question, hope to have a concise answer Given that the curve C: y = x3-3x2 + 2x, the line L: y = KX, and the line L and the curve C are tangent to the point (x0, Y0) (x0 ≠ 0), the equation and tangent point coordinates of the line L are obtained
13. If the line y = x is the tangent of the curve y = x3-3x2 + ax, then a=______ ．
14. If the line y = x is the tangent of the curve y = x3-3x2 + ax, then a=______ ．
15. Given y = 2x + if the line y = KX + B is symmetric to the given line about the Y axis, find the values of K and B
16. It is known that the image of a function y = KX + B passes through a point (- 2,5), and the intersection of the line y = - 3 / 2x + 3 and the Y axis is symmetric about the X axis Find the analytic expression of this function
17. As shown in the figure, the left and right fixed points of ellipse C1: x ^ 2 / 4 + y ^ 2 / 3 = 1 are a, B and P respectively, which are a point on the right branch (above the X axis) of hyperbola C2: x ^ 2 / 4-y ^ 2 / 3 = 1 Connecting AP is called C1 to C, connecting Pb and extending the intersection C1 to D, and the areas of △ ACD and △ PCD are equal. Calculate the slope of the straight line PD and the inclination angle of the straight line CD
18. Given the hyperbola c1:2x ^ 2-y ^ 2 = 1, let the ellipse c2:4x ^ 2 + y ^ 2 = 1, if M and N are the moving points on C1 and C2 respectively, and OM is perpendicular to on, we prove that: The distance from O to the straight line Mn is a fixed value
19. It is known that hyperbola C1 and hyperbola C2: y ^ 2 / 4-x ^ 2 / 9 = 1 have the same asymptote And through the point m (9 / 2, - 1), the standard equation of hyperbola C1 is obtained
20. Given that the two intersections of two curves y = KX + 1 and x ^ 2-y-8 = 0 are symmetric about the Y axis, then the coordinates of the two intersections are