At what point does the curve have maximum curvature? y = 4ex (x, y) = what happens to the curvature as x → ∞? κ(x) approaches as x → ∞.

Answer-

At the curve has maximum curvature.

Solution-

The formula for curvature =

Here,

Then,

Putting the values,

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

Now, equating this to 0

Solving this eq,

we get

∴ At   the curvature is maximum.

if x decreases by 4 then y increases by 10

step-by-step explanation:

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076