The equation of the tangent line is y = 7x -1
How to find equation of tangent line.
The equation of the tangent line to the graph f(x) = (x² + 2)(x + 1) at the point (1, 6)\), follow these steps:
Find the derivative f'(x) to find the slope of the tangent at x= 1
f(x) = (x² + 2)(x + 1)
f'(x) = (2x)(x + 1) + (x² + 2)(1)
Calculate the derivative of f(x)
When x = 1
f'(1) = (2)(2) + (3)(1)
= 4 + 3
= 7
Use the point-slope form of the equation of a line: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point, and m, is the slope.
y -6 = 7(x -1)
y - 6 = 7x -7
y = 7x -7 + 6
y = 7x -1
Therefore, the equation of the tangent line is y = 7x -1