The tangent to the curve y = x2 + 3x will pass through the point 0, - 9 if it is drawn at the point
Answers
Answer:
points ( 3 , 18) & (-3 , 0)
Step-by-step explanation:
The tangent to the curve y = x2 + 3x will pass through the point 0, - 9 if it is drawn at the point
y = x² + 3x
dy/dx = 2x + 3
Tangency point = (x , x² + 3x)
slope to point (0 , -9)
= ( x² + 3x +9)/x
( x² + 3x +9)/x = 2x + 3
=> x² + 3x +9 = 2x² + 3x
=> x² = 9
=> x = ±3
y = 18 , 0
points ( 3 , 18) & (-3 , 0)
Answer:y=3x-9
Step-by-step explanation:
In order to find the equation of the tangent to the the cure,y= x² +3x at point, (0,-9), we need to find the gradient function: y¹= 2x+3
At (0,-9); the gradient is : (2×0)+3
=3
Finally, we determine the equation of a straight line passing through point (0,-9) and has a gradient of 3
Thus, y+9/x=3
y+9=3x
y=3x-9
Therefore,the equation of the tangent to the curve is y=3x-9