Find the slope of the tangent to curve y = x³ - 3x + 2 at the point whose x-coordinate is 3

Solution:

For a curve y = f(x) containing the point (x₁,y₁) the equation of the tangent line to the curve at (x₁,y₁) is given by 

y − y₁ = f′(x₁) (x − x₁).

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The given curve is y = x³ - 3x + 2

Therefore,

dy/dx = d/dx (x³ - 3x + 2)

= 3x² - 3

Now, the slope of the tangent at the point where the x-coordinate is 2 is given by,

dy/dx]_{x = 2} = 3x² - 3]_{x = 2}

= 3(3)² - 3

= 27 - 3

= 24

Therefore, the slope of the tangent is 24

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 4

Find the slope of the tangent to curve y = x³ - 3x + 2 at the point whose x-coordinate is 3.

Summary:

The slope of the tangent to curve y = x³ - 3x + 2 at the point whose x-coordinate is 3 is 24. The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line