Calculus Answers

Determine the focus and directrix of the parabola with the given equation. Sketch the graph, indicate the focus, vertex and axis of symmetry.

1. x² - 6x - 5y = -34

2. y² - 12x + 8y = -40

1. Find the derivative of the given function, f(x)=1966

2. Find the derivative of the following function: f(x)=x²+6x+9

3. Find the slope of the tangent line to the graph of the following function at the indicated point, f(x)=3-2x at (-1, 5)

4. Find the derivative of the function: f(x)=x½

5. Find the derivative of the function f(x)=5x²(x+47)

6.) Find the derivative of the function: f(x)=5(x+47)²

7. Find the derivative of the function f(x)= 5x²/(x+47).

8. Which of the following functions are NOT differentiable?

a. f(x)=lxl

b. f(x)=(x+3)⁴

c. f(x)=mx+b

d. f(x)=1066

e. none of the above

9. Which of the following functions are NOT everywhere continous?

a. f(x)=x²-4/(x+2)

b. f(x)=(x+3)⁴

c. f(x)=1066

d. f(x)=mx+b

e. none of the above

Find the slope of the tangent line of the given function f below.

f(x)=x²+1

Find the slope of the tangent line of the given function f below.

f(x)=x²+1

Find the equation of the tangent line to each curve when x has a given value.

1. f(x)= x²+2 as x= 2

2.f(x)= 3x²+1 as x=1

Find the slope of the tangent line of the given function f below.

1.f(x)=2x+5

2.f(x)=x²-1

Differentiate the following functions. Show step by step solution and

Indicate your final answer.

1. X = 1/t

2. y = 4x²– 3x – 2

3. y = (x+2) ^1/2

Our hypothetical population contains the scores 4, 6, 7, and 9. Determine

the mean and variance of the sampling distribution of the sample mean,

given that samples contain two scores drawn from the population with

replacement?

The volume, V cm³, of a metallic cube of side length x cm, is increasing at the constant rate of 0.216 cm3 s^-1 .

a)Determine the rate at which the side of the cube is increasing when the side length reaches 6 cm.

b) Find the rate at which the surface area of the cube, A cm², is increasing when the side length reaches 6 cm.

Find the dy/dx and simply the result, if possible

a. y=√x-1/√x

b. y=x²+π²+xπ

c.y=x² sec x

d.y=sinx-1/cosx

e.y=1/ex+2

a) Find 𝑑𝑦

𝑑𝑥

𝑔𝑖𝑣𝑒𝑛 𝑡ℎ𝑎𝑡 𝑦 = (𝑥

2 – 3x + 1)4

b) Differentiate 2

𝑥(x)−3𝑥+1

c) Intergrate 2x2 2