Calculus Answers

F(x) = 4x² + 6x

Find the dy/dx of each of the following:

1.y=〖5x〗^3-〖4x〗^2+3x-6

2.y=∛x+4/x+√x

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

4.y=(x^2+1)(x+5+1/x)

5.y=(5x+1)/(2√x)

Determine whether if

lim f(c) = f(c)

x→c

1. f(x) = x+2; c = -1

2. f(x) = x-2; c = 0

3. (at c = -1 )

f(x) = {x ² - 1 if x < -1}

f(x) = { (x - 1) ² - 4 if x ≥ -1}

4. (at c = 1 )

f(x) = {x³ - 1 if x < 1}

f(x) = { x² + 4 if x ≥ 1}

Determine whether if lim f(c) = f(c)

x→c

1. f(x) = x+2; c = -1

2. f(x) = x-2; c = 0

3. (at c = -1 )

f(x) = {x ² - 1 if x < -1}

f(x) = { (x - 1) ² - 4 if x ≥ -1}

4. (at c = 1 )

f(x) = {x³ - 1 if x < 1}

f(x) = { x² + 4 if x ≥ 1}

Step by step solution on how to find the slope of the tangent line of the given function f below.

1. f(x)=2x+5

2. f(x)=x²+1

3. f(x)=x²-1

1. Determine the center and radius given the equation of a circle in standard form.

1. (x-5)+(y + 4)² = 64

2. (x + 9) +(y-7)² = 121

3. x² + (y+6)² = 4

4. (x-1)² + y² = 1

• II. Convert the equation of a circle in standard form to general form or vice versa.

1. (x-2)² + (y+6)² = 4 2. (x+6)² + (y + 4)² = 36

3. x² + y² + 4x-2y-4=0

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