expression into the area formula. First isolate y = , then plug in: A = x^2 + 4x = x^2 + . Now we take the derivative A′ = 2x −
Set the derivative equal to zero and solve:2 x − = 02 x^3 − 2000 = 0x^3 = 1000x = 10 ftThe dimensions of the base are 10 feet by 10 feet.- First, we need to find the slope of the tangent line to y = . This is the derivative: y′ =
. Now, to find where the slope is the greatest, we take the derivative and set it equal
to zero. We get y′′ = = 0, which can be simplified to = 0.
Note that we just need to solve for where the numerator is 0. Let’s simplify the numerator:−2 − 2x^2 + 8x^2 = 0
−2 + 6x^2 = 0We can solve for x: x = ± . If we plug these two values into the equation for the slope wefind that at x = , y′ =