Calculus plus 1 test

$$f\left(x\right)=\frac{6x^4-4x^2-8x+2}{2x^2}$$

find $$f'\left(x\right)$$

$$y=5\sqrt[3]{x}-\frac{2}{\sqrt[3]{x}}+4\sqrt[2]{x^5}$$

find $$\frac{dy}{dx}$$

Write your answer in radical form

The graph is of $$f'\left(x\right)$$ Find the intervals where $$f\left(x\right)$$ is increasing and decreasing.
Decreasing from ​ (a)   and ​ (b)  

Increasing from ​ (c)   and​ (d)  

Find the equation of a tangent line to $$y=5-4x-3x^2$$ at $$x=-1$$

Find the equation of a normal line to $$y=5-4x-3x^2$$ at $$x=-1$$

The equation $$h\left(x\right)=x^4-\frac{8}{3}x^3-6x^2-4$$ has 3 local max/mins.

Find and label all 3 local max/mins coordinates (x , y)

(like Min: and max: )

must use calculus to get full credit

Determine $$\int_0^480-x^3dx$$  using an estimate of 4 equivalent based trapezoids

Show your table values, and math to get final answer for full credit

(a)  

$$\int_1^9x^2-\sqrt[]{x}\ dx\ =$$

(a)  

find the equation of the following graph

An open box is to be made from a 30 inch by 30 inch square piece of material by cutting equal squares (x sides) from the corners and turning up the sides.

Write the volume equation of this open box in terms of x