# Calculus

posted by .

What is the 4 step process when finding the slope of the tangent line at any given point?

• Calculus -

Example of 4 step process

f(x) = -1/2(x^2)

Step 1
f(x + h)= -1/2(x + h)^2
f(x + h)= -1/2(x^2 + 2xh + h^2)
f(x + h)= -1/2 x^2 - xh - 1/2 h^2

Step 2
f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 - (-1/2 x^2)

f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 + 1/2 x^2

f(x + h) - f(x) = -xh - 1/2 h^2
f(x + h) - f(x) = h (-x - 1/2 h)

Step 3
(f(x + h) - f(x))/h = (h(-x - 1/2 h))/h
(f(x + h) - f(x))/h = -x - 1/2 h

Step 4
Evaluate lim h-->0
lim h-->0 = -x - 1/2 (0)
lim h-->0 = -x

Dx(-1/2 x^2) = -x

• Calculus -

Evaluate log4 1/3ã16 step by step solution

## Similar Questions

1. ### Pre Calculus

please help me with this problem? I don't know how ro do it. please show me step by step. Write the slope intercept form the equations of the lines through the given point parallel to the given line and (B) perpendicular to given line.
2. ### Calculus

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). …
3. ### calculus

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = 2x^2 + 7x
4. ### Math

What are is the 4 step process when finding the slope of the tangent line at any given point?

Use the four step process to find the slope of the tangent line to the graph at any point: f(x) = -1/2(x^2)
6. ### Calculus [finding slope of tangent line]

Find the slope of the tangent line to the curve 0x^2−2xy+2y^3=10 at point (-4,1) Help please?
7. ### Applied Calculus......

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x-5x^2 at (-2, -32) I have to use the four step process, but seem to be getting stuck...
8. ### Calculus

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = 16 - 10 x Step 2: f(x + h) - f(x) = Step 4: f'(x) = lim(h->0)(f(x + h)- f(x))/h =
9. ### calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)
10. ### Calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)

More Similar Questions