Question

True or False The slope of the tangent line to the graph of fat $\left(c,f\left(c\right)\right)$ is the derivative of f at c.

Short answer

The given statement is true.

Step-by-step solution

Step 1. Given Information

The slope of the tangent line through a point on the graph of a function provides the function's instantaneous rate of change at that point.

Step 2. Determining whether the given statement is true or false

The given statement "the slope of the tangent line to the graph of fat$(c,f(c\left)\right)$ is the derivative of f at c" is true because the slope of the tangent line of a function at a given point is defined by the derivative of the function at the given point.