What is the slope of the tangent to the curve of f(x) at x = 6 for the function f(x) = 3x^3 + 6x^2 - 10x + 4?

What is the slope of the tangent to the curve of f(x) at x = 6 for the function f(x) = 3x^3 + 6x^2 - 10x + 4?

• A. 256
• B. 386
• C. 496
• D. 56

Answer: (B)

To find the slope of the tangent to the curve at a specific point, you first need to determine the derivative of the function. The derivative of a function represents the slope of the tangent line at any given point on the curve. Given the function \( f(x) = 3x^3 + 6x^2 - 10x + 4 \), you can calculate its derivative using power rule. The derivative \( f'(x) \) is calculated as follows: 1. The derivative of \( 3x^3 \) is \( 9x^2 \). 2. The derivative of \( 6x^2 \) is \( 12x \). 3. The derivative of \( -10x \) is \( -10 \). 4. The derivative of the constant \( 4 \) is \( 0 \). Putting this all together, we have: \[ f'(x) = 9x^2 + 12x - 10 \] Next, to find the slope of the tangent line at \( x = 6 \), substitute \( 6 \) into the derivative: \[ f'(6) = 9(6)^2 + 12(6) -

To find the slope of the tangent to the curve at a specific point, you first need to determine the derivative of the function. The derivative of a function represents the slope of the tangent line at any given point on the curve.

Given the function ( f(x) = 3x^3 + 6x^2 - 10x + 4 ), you can calculate its derivative using power rule. The derivative ( f'(x) ) is calculated as follows:

1. The derivative of ( 3x^3 ) is ( 9x^2 ).

2. The derivative of ( 6x^2 ) is ( 12x ).

3. The derivative of ( -10x ) is ( -10 ).

4. The derivative of the constant ( 4 ) is ( 0 ).

Putting this all together, we have:

[ f'(x) = 9x^2 + 12x - 10 ]

Next, to find the slope of the tangent line at ( x = 6 ), substitute ( 6 ) into the derivative:

[ f'(6) = 9(6)^2 + 12(6) -