find an equation of the line tangent to the graph of f(x)=2x^3 at (1,2).\nthe equation of the tangent line…

find an equation of the line tangent to the graph of f(x)=2x^3 at (1,2).\nthe equation of the tangent line is y = .\n(type an expression using x as the variable.)

find an equation of the line tangent to the graph of f(x)=2x^3 at (1,2).\nthe equation of the tangent line is y = .\n(type an expression using x as the variable.)

Answer

Explanation:

Step1: Find the derivative

$f'(x)=6x^{2}$

Step2: Evaluate the derivative at $x = 1$

$f'(1)=6(1)^{2}=6$ (slope of tangent)

Step3: Use point - slope form

$y - 2=6(x - 1)$

Step4: Simplify

$y=6x-4$

Answer:

$y = 6x - 4$