Chapter 14: Q. 3 (page 896)

If $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ exists, it equals the slope of the __ _ to the graph of f at the point $(c, f (c)) .$

Short Answer

Expert verified

If $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ exists, it equals the slope of thetangentlineto the graph offat the point $(c, f (c)) .$

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. Filling the blank

As we know the tangent of a line to the graph of the function $f (x)$ at the point $(c, f (c))$ has a slope of $\lim_{x \to c} \frac{f (x) - f (c)}{x - c} .$

So, if $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ exists, it equals the slope of the tangent line to the graph offat the point $(c, f (c)) .$

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If $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ exists, it equals the slope of the __ _ to the graph of f at the point $(c, f (c)) .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Filling the blank

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If limx→cf(x)-f(c)x-cexists, it equals the slope of the ______ _____ to the graph of f at the point c,fc.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Filling the blank

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Most popular questions from this chapter

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If $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ exists, it equals the slope of the __ _ to the graph of f at the point $(c, f (c)) .$