Question

at what value(s) of x on the curve y=−2 40x3−3x5 does the tangent line have the largest slope? answer (separate by commas): x=

Answer 1

The value(s) of x on the curve y = -240x³ - 3x⁵ at which the tangent line has the largest slope can be found by setting the derivative of y with respect to x equal to zero and solving for x .

Step-by-step explanation:

To find the value(s) of x at which the tangent line has the largest slope, we need to find the critical points of the curve. The slope of the tangent line is given by the derivative of y with respect to x . Therefore, we set the derivative equal to zero to find where the slope is either a maximum or minimum.

The given function is y = -240x³ - 3x⁵. To find the derivative dy/dx we apply the rules of differentiation. After finding the derivative, we set it equal to zero and solve for x to identify the critical points.

Once we obtain the values of x from solving the derivative equation, we can provide the answer in the required format, separating multiple values by commas. These critical points correspond to the x values at which the tangent line to the curve has the largest slope.

Answer 2

To find the value(s) of x on the curve y = -240x3 - 3x5 where the tangent line has the largest slope, find the derivative of y with respect to x, set it equal to zero, and solve for x. The resulting values of x are the ones where the tangent line has the largest slope.

Step-by-step explanation:

To find the value(s) of x on the curve y = -240x3 - 3x5 where the tangent line has the largest slope, we need to find the maximum slope of the tangent line.

We can start by finding the derivative of y with respect to x, which gives us dy/dx = -720x2 - 15x4.

To find the critical points where the slope is maximized, we set the derivative equal to zero and solve for x: -720x2 - 15x4 = 0.

Solving for x, we find x = 0 and x = ±sqrt(48/9). Therefore, the value(s) of x where the tangent line has the largest slope are x = 0, x = sqrt(48/9), and x = -sqrt(48/9).