Find the slope of the tangent to the curve y = 3x⁴ - 4x at x = 4

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 = 3x⁴ - 4x at x = 4.

Then,

the slope of the tangent to the given curve at x = 4 is given by,

dy/dx]_{x = 4} = d/dx (3x⁴ - 4x)]_{x = 4}

= 12x³ - 4]_{x = 4}

= 12 (4)3 - 4

= 12 (64) - 4

= 764

Therefore, the slope of the tangent is 764

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 1

Find the slope of the tangent to the curve y = 3x⁴ - 4x at x = 4

Summary:

The slope of the tangent to the curve y = 3x⁴ - 4x at x = 4 is 764. The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line