assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28

Given:

x and y are both differentiable functions of t.

To find:

The value of .

Solution:

We have,

      ...(i)

At x=-1,

Divide both sides by 3.

Taking cube root on both sides.

So, y=2 at x=-1.

Differentiate (i) with respect to t.

Putting x=-1, y=2 and , we get

Divide both sides by -8.

Therefore, the value of is 36.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1