# How to find the indicated quantities for f(x) = 3x^2?

##### 1 Answer

A) Slope =

B) Slope = 6

C)

#### Explanation:

We have

**A. Slope of Secant Line**

The slop of the secant line is given by:

# (Delta y)/(Delta x) = {f(1+h)-f(1)}/{(1+h)-(1)}#

# \ \ \ \ \ \ \ = {3(1+h)^2-3}/{h}#

# \ \ \ \ \ \ \ = {3(1+2h+h^2)-3}/{h}#

# \ \ \ \ \ \ \ = {3+6h+3h^2-3}/{h}#

# \ \ \ \ \ \ \ = {6h+3h^2}/{h}#

# \ \ \ \ \ \ \ = 6+3h#

**B. Slope of the graph (tangent) at **

If wd take the limit of the slope at the secant line (A) then by the definition of the derivative then in the limit as

# lim_(h rarr 0) 6+3h = 6 #

**C. Equation of tangent**

Th slope of the tangent is

# \ \ \ \ \ y-3 = 6(x-1) #

# :. y-3 = 6x-6 #

# :. \ \ \ \ \ \ \ y = 6x-3 #

Which we can confirm via a graph:

graph{ (y-3x^2)(y-6x+3)=0 [-5, 5, -2, 10]}