Question

5. Find the equation of the tangent line to the curve
y= 10xe^x at the point (0,0). The equation of this tangent line
can be written in the form y=mx+b. Find m and b.​

Answer 1

Answer:

m = 10 , b = 0

Step-by-step explanation:

y = 10xe^x

The slope of the tangent to a curve at any point is determined by differentiating it w.r.t x,

dy/dx = 10(e^x + xe^x)

m = dy/dx | (0,0) = 10(e^0 + 0e^0) = 10(1) = 10

Since, (0,0) are the coordinates of the origin, thus the tangent cuts the y-axis at (0,0) hence, the y-intercept b = 0.

Therefore, m = 10 and b = 0.

Answer 2

Answer:

m = 10 , b = 0

Step-by-step explanation:

y = 10xe^x

The slope of the tangent to a curve at any point is determined by differentiating it w.r.t x,

dy/dx = 10(e^x + xe^x)

m = dy/dx | (0,0) = 10(e^0 + 0e^0) = 10(1) = 10

Since, (0,0) are the coordinates of the origin, thus the tangent cuts the y-axis at (0,0) hence, the y-intercept b = 0.

Therefore, m = 10 and b = 0.