Question

given a function and its derivative, find the slope of the line tangent to the graph of the function at x = 0. f(x)=2x^3 f(x)=6x^2 the slope of the tangent line at the indicated value of x is

Explanation:

Step1: Recall tangent - slope relationship

The slope of the tangent line of a function at a point is the value of the derivative at that point.

Step2: Substitute x = 0 into derivative

Substitute \(x = 0\) into \(f'(x)=6x^{2}\), we get \(f'(0)=6\times0^{2}\).

Step3: Calculate the result

\(6\times0^{2}=0\).

Answer:

0