Question

A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x. dx y = 4x2 + 7; = 4 centimeters per second dt

x = -1
DY/DT =

Answer 1

To find dy/dt, differentiate the given function with respect to time using the chain rule. Substitute the value of x to find the value of dy/dt.

Step-by-step explanation:

To find dy/dt, we need to differentiate the given function with respect to time. In this case, the function is y = 4x^2 + 7. Differentiating both sides of the equation, we get dy/dt = d(4x^2 + 7)/dt.

Next, we need to use the chain rule to differentiate the function. The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x), where f'(x) represents the derivative of f(x) and g'(x) represents the derivative of g(x).

In this case, f(x) = 4x^2 + 7 and g(x) = x. Taking the derivatives, we have f'(x) = 8x and g'(x) = 1. Therefore, dy/dt = f'(g(x)) * g'(x) = (8x) * (1) = 8x.

Now, we can substitute the given value of x (-1) into the equation to find the value of dy/dt. dy/dt = 8(-1) = -8 centimeters per second.