If there is a line passing through the point (1,0) tangent to the curves y = x ^ 3 and y = ax ^ 2 + 15 / 4-9, how to calculate a

If there is a line passing through the point (1,0) tangent to the curves y = x ^ 3 and y = ax ^ 2 + 15 / 4-9, how to calculate a

First, find the straight line passing through point (1,0) and the straight line of curve y = x ^ 3
At the same time, the tangent is also tangent to y = ax ^ 2 + 15 / 4x-9
Step 1: set the tangent point with curve y = x ^ 3 as (x0, Y0), and release x0
Step 2: let the tangent point of curve y = ax ^ 2 + 15 / 4x-9 be (x1, Y1) to solve

If there are straight lines and curves passing through points (1, 0), y = X3 and y = AX2 + 15 4x-9 are tangent, then a is equal to _

From y = x3 ⇒ y '= 3x2, let the tangent equation at any point (x0, X03) on curve y = X3 be y-x03 = 3x02 (x-x0), (1, 0) be substituted into the equation to obtain x0 = 0 or x0 = 3
two
① When x0 = 0, the tangent equation is y = 0, then AX2 + 15
4x-9=0，△=(15
4)2-4a × (-9)=0⇒a=-25
sixty-four
② When x0 = 3
2, the tangent equation is y = 27
4x-27
4. By
y=ax2+15
4x-9
y=27
4x-27
four ⇒ax2-3x-9
4=0，△=32-4a(-9
4)=0⇒a=-1∴a=-25
64 or a = - 1
So the answer is: - 25
64 or - 1

Find the derivative of F (x) = ln (2-x) + ax

(ln(2-x))'=(2-x)'*(1/(2-x))=-1/(2-x)=1/(x-2)
ax=a
f'(x)=1/(x-2)+a
This involves the derivation of composite functions
Suppose f (x) = ln (1-x)
Let g (x) = 1-x, C (x) = ln (g (x))
f'(x)=g'(x)*c'(x)=-1*1/g(x)=1/(x-1)

What is the derivative of LN x + ln (2-x) + ax

(ln(2-x))'=(2-x)'*(1/(2-x))=-1/(2-x)=1/(x-2)
ax=a
f'(x)=1/(x-2)+a
This involves the derivation of composite functions
Suppose f (x) = ln (1-x)
Let g (x) = 1-x, C (x) = ln (g (x))
f'(x)=g'(x)*c'(x)=-1*1/g(x)=1/(x-1)

Find the derivative of F (x) = ln (AX) 1. The images of Ln (AX) are different. It looks different The integral of 2 1 / X is LNX + C, not ln (AX) + C

Answer 1 / X
Two approaches:
1. Derivative step by step. First, the overall derivative of Ln (AX) is 1 / ax, and then the derivative of ax is a, so (1 / ax) * a = 1 / X
2. (this method is not rigorous enough) first deform f (x) = ln (AX) = LNA + LNX to obtain 0 + 1 / x = 1 / X

1ogx derivative is a formula? Thank you very much for sending the formula table!

1ogx is lgx?
Derivative formula:
(㏒x)'=1/x
In addition, ㏒ ax derivative formula:
(㏒aX)’=1/(xlna)