Slope of a Curve at a Point
Key Questions

The slope of a curve of
#y=f(x)# at#x=a# is#f'(a)# .Let us find the slope of
#f(x)=x^3x+2# at#x=1# .By taking the derivative,
#f'(x)=3x^21# By plugging in
#x=1# ,
#f'(1)=3(1)^21=2# Hence, the slope is
#2# . 
First you need to find
#f'(x)# , which is the derivative of#f(x)# .#f'(x)=2x0=2x# Second, substitute in the value of x, in this case
#x=1# .#f'(1)=2(1)=2# The slope of the curve
#y=x^23# at the#x# value of#1# is#2# . 
Answer:
See below
Explanation:
In every courve's point , the slope of a courve is defined by the tangent line in that point. See picture
Questions
Derivatives

Tangent Line to a Curve

Normal Line to a Tangent

Slope of a Curve at a Point

Average Velocity

Instantaneous Velocity

Limit Definition of Derivative

First Principles Example 1: x²

First Principles Example 2: x³

First Principles Example 3: square root of x

Standard Notation and Terminology

Differentiable vs. Nondifferentiable Functions

Rate of Change of a Function

Average Rate of Change Over an Interval

Instantaneous Rate of Change at a Point