# How to find the slope of a curve at a given point?

The slope of a curve is a slope of a tangent line for a curve at one point.

## Answer: To find the slope of a curve at a given point, we simply differentiate the equation of the curve and find the first derivative of the curve, i.e., dy/dx.

Let's find out the answer with an example.

**Explanation:**

To determine slope, we use the following steps:

- Firstly, we need to differentiate the given equation or simply we have to find dy/dx of an equation.
- After differentiating we will get the equation of slope.
- Put the value of x in the equation to determine the slope.

Let's take an example to find the slope of a curve at a given point.

**Example:** Determine the slope of the curve y = x^{3} − x^{2} + 1 at the given point (2,−15).

Given,

Equation ⇒ y = x^{3} − x^{2} + 1,

Point = (2,−15)

First we need to differentiate the given equation (y = x^{3} − x^{2} + 1),

dy/dx = d(x^{3} − x^{2} + 1)/dx

dy/dx = d(x^{3})/dx − d(x^{2})/dx + d(1)/dx

dy/dx = 3x^{2} – 2x

Now, put the value of (x = 2) in the equation to determine the slope.

dy/dx = 3(2)^{2} – 2(2)

dy/dx = 8

Thus, 8 is the slope of the given curve.