Find an equation of the tangent line to the graph of f at the given point. ,at

Question

​Find an equation of the tangent line to the graph of f at the given point. ​  ,at  ​

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function at the given point and then use the point-slope form of a line.

The derivative of f(x) is f'(x) = 4x^3 - 12x^2 + 10. Therefore, the derivative at the point (2,6) is f'(2) = 4(2)^3 - 12(2)^2 + 10 = 18.

Using the point-slope form of a line, the equation of the tangent line at (2,6) is y - 6 = 18(x - 2), which simplifies to y = 18x - 30.

Therefore, the answer is D.

​Find an Equation of the Tangent Line to the Graph

Find an Equation of the Tangent Line to the Graph