The given curve is y = 5x - 2x^2.

First, we need to find the derivative of the curve to get the slope.

The derivative of y = 5x - 2x^2 is dy/dx = 5 - 4x.

At x = 3, the slope of the curve is dy/dx = 5 - 4*3 = -7.

Now, we need to find the rate at which the slope of the curve is changing. This is given by the second derivative of the curve.

The second derivative of y = 5x - 2x^2 is d^2y/dx^2 = -4.

This means the slope of the curve is decreasing at a rate of 4 units/sec^2.

However, since x is increasing at a rate of 2 units/sec, we need to multiply the rate of change of the slope by the rate of change of x to get the rate of change of the slope with respect to time.

So, the slope of the curve is changing at a rate of -4 * 2 = -8 units/sec^2 at x = 3.

Question

The given curve is y = 5x - 2x^2.

First, we need to find the derivative of the curve to get the slope.

The derivative of y = 5x - 2x^2 is dy/dx = 5 - 4x.

At x = 3, the slope of the curve is dy/dx = 5 - 4*3 = -7.

Now, we need to find the rate at which the slope of the curve is changing. This is given by the second derivative of the curve.

The second derivative of y = 5x - 2x^2 is d^2y/dx^2 = -4.

This means the slope of the curve is decreasing at a rate of 4 units/sec^2.

However, since x is increasing at a rate of 2 units/sec, we need to multiply the rate of change of the slope by the rate of change of x to get the rate of change of the slope with respect to time.

So, the slope of the curve is changing at a rate of -4 * 2 = -8 units/sec^2 at x = 3.

Knowee AI · Accepted Answer

The given curve is y = 5x - 2x^2.

First, we need to find the derivative of the curve to get the slope.

The derivative of y = 5x - 2x^2 is dy/dx = 5 - 4x.

At x = 3, the slope of the curve is dy/dx = 5 - 4*3 = -7.

Now, we need to find the rate at which the slope of the curve is changing. This is given by the second derivative of the curve.

The second derivative of y = 5x - 2x^2 is d^2y/dx^2 = -4.

This means the slope of the curve is decreasing at a rate of 4 units/sec^2.

However, since x is increasing at a rate of 2 units/sec, we need to multiply the rate of change of the slope by the rate of change of x to get the rate of change of the slope with respect to time.

So, the slope of the curve is changing at a rate of -4 * 2 = -8 units/sec^2 at x = 3.

For the curve ݕ = 5ݔ − 2ݔଷ ,if ݔ increases at the rate of 2units/sec, then atݔ = 3the slope of the curve is changing at

Question

For the curve $y = 5x - 2x^2$ , if $x$ increases at the rate of 2 units/sec, then at $x = 3$ the slope of the curve is changing at

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